Your basic problem is in function
void readIntFile(ifstream& x, int intArray[], int size, int& length)
You do not set the output variable length. And you use the wrong index value for your array. Please check.
Additionally there are many other problems in your code.
I will now paste your code, amended with my comments comments, where problems are or where things should be improved.
Please see:
#include<iostream>
#include<iomanip>
#include<fstream>
#include<string>
#include<assert.h>
using namespace std;    // Should never be used. Always use fully qualified names
const int SIZE = 20;    // Please use constexpr
// Do not use C-Style function prototypes. Put main at the bottom
// Do not use C-Style Arrays
// In C++ (C-Style-)Arrays are different. You actually do not pass an array to your function
// but a decyed pointer. You can pass an array by pointer or by reference, but this has a different syntax
void readIntFile(ifstream& x, int intArray[], int size, int &length);
void printValues(int intArray[], int& length);
char getSentinel();
int main()
{
    // All variables shall be initialized at the point of defintion
    ifstream inputStream;   // You should define variables just before you need then
    const int size = SIZE;  // This is code duplication. And constexpr should be used
    string fileName;
    int length = 0;
    bool isEmpty = false;
    int intArray[size];   // C-Style Arrays should not be used. Use std::array or best, std::vector
    char sentinel = 'y';  // You could use universal initializer syntax with braced initializer
    while (sentinel == 'y' || sentinel == 'Y')
    {
        cout << "Please enter the name of the file: ";
        cin >> fileName;
        inputStream.open(fileName);   // The constructor can open the file for you
        if (inputStream.bad() || inputStream.fail()) // This is too complicated
        {
            cout << "Error, <" << fileName << "> is Invalid File Name.";
        }
        if (fileName.empty())  // Check is too late and not necessary
        {
            isEmpty = true;
        }
        if (isEmpty == true)
        {
            cout << "Error <" << fileName << "> has no data.";
        }
        if (inputStream.good() && isEmpty == false)
        {
            readIntFile(inputStream, intArray, size, length);
            printValues(intArray, length);
            inputStream.close();  // Destructor will clsoe the file for you
        }
        sentinel = getSentinel();
    }
    return 0;
}
// Not optimal function prototype
void readIntFile(ifstream& x, int intArray[], int size, int& length)
{
    // the whole design / logic is very strange
    int count = 0; 
    int arrayLocation = -1; // More then strange. Shows that this is a bad design
    int fileInputValue = 0;
    x >> fileInputValue;
    while (!x.eof())        // Bad or even wrong design
    {
        count ++;   // Wrong. See below. array will be filled with starting with index one
        if (count > SIZE)
        {
            cout << "The file has more than <" << SIZE << "> values." << endl;
            break;
        }
        else
        {
            arrayLocation ++;   // This variable is not used
            intArray[count] = fileInputValue;
            x >> fileInputValue;
        }
    }
    // Nobody will set the length variable
}
void printValues(int intArray[], int& length)
{
    assert(length > 0); // Basically OK, but no necessary here. Cannoz happen
    cout << "<" << length << "> values processed from the file. The values are: ";
    for (int i=0; i <= length; i++)
    {
        cout << intArray[i] << ", ";
    }
    // There is now newline character used anywhere
}
// Very complicated
char getSentinel()
{
    char userInput = 'n';
    bool inputCheck = false;
    cout << "Do you wish to process another file (y/n)?" << endl;
    cin >> userInput;
    do
    {
        if (userInput == 'y' || userInput == 'Y' || userInput == 'n' || userInput == 'N')
        {
            inputCheck = true;
        }
        else
        {
            cout << "Invalid response: <" << userInput << ">" << endl;
            cout << "Do you wish to process another file (y/n)?" << endl;
            cin >> userInput;
        }
    } while (!inputCheck);
    return userInput;
}
Next, I will make your code working, by fixing the biggest problems. I will still follow your programming style.
#include<iostream>
#include<iomanip>
#include<fstream>
#include<string>
#include<assert.h>
constexpr int MaxArraySize = 20;
using IntArray = int[MaxArraySize];
void readIntFile(std::ifstream& x, int intArray[], int& length)
{
    length = 0;
    int value{};
    while (x >> value)
    {
        if (length >= MaxArraySize)
        {
            std::cout << "The file has more than <" << MaxArraySize << "> values.\n";
            break;
        }
        else
        {
            intArray[length++] = value;
        }
    }
}
void printValues(int intArray[], int& length)
{
    std::cout << "\n<" << length << "> values processed from the file. The values are: ";
    for (int i=0; i < length; i++)
    {
        std::cout << intArray[i] << ", ";
    }
    std::cout << "\n\n";
}
bool getSentinel()
{
    char userInput{'n'};
    bool valid = false;
    while (not valid)
    {
        std::cout << "\n\nDo you wish to process another file (y/n)?\n";
   
        std::cin >> userInput;
        if (userInput != 'y' && userInput != 'Y' && userInput != 'n' && userInput != 'N')
        {
            std::cout << "Invalid response: <" << userInput << ">\n\n";
        }
        else {
            valid = true;
        }
    }
    return ( userInput=='y' || userInput=='Y');
}
int main()
{
    
    int intArray[MaxArraySize];
    
    bool sentinel = true;
    while (sentinel)
    {
        std::cout << "Please enter the name of the file: ";
        
        std::string fileName{};
        std::cin >> fileName;
        if (fileName.empty())
        {
            std::cout << "Error <" << fileName << "> has no data.\n\n";
        }
        else {
            std::ifstream inputStream(fileName);
            if (!inputStream)
            {
                std::cout << "Error, <" << fileName << "> is Invalid File Name.\n\n";
            }
            else 
            {
                int length = 0;
                readIntFile(inputStream, intArray, length);
                printValues(intArray, length);
            }
        }
        sentinel = getSentinel();
    }
    return 0;
}
and, in the end, because we are in a C++ site here, I will show (one of many possible) a more advanced C++ solution.
This is just for information and to grab some ideas for the future
#include<iostream>
#include<iomanip>
#include<fstream>
#include<string>
#include<vector>
#include<algorithm>
#include<iterator>
#include<initializer_list>
// Some aliases for easier reading and saving typing work
using DataType = int;
using Vector = std::vector<DataType>;
// Define an "in" operator
struct in {
    in(const std::initializer_list<char>& il) : ref(il) {}
    const std::initializer_list<char>& ref;
};
bool operator,(const char& lhs, const in& rhs) {
    return std::find(rhs.ref.begin(), rhs.ref.end(), lhs) != rhs.ref.end();
}
int main() {
    
    // As long as the user wants to read files
    for (bool userWantsToContinue{true}; userWantsToContinue;) {
        
        std::cout << "\nPlease enter a valid filename:  ";
        if (std::string filename{}; std::cin >> filename) {
            
            // Open the file for reading and check, it it is open
            if (std::ifstream inputStream{filename}; inputStream) {
                
                // Read all data from the file    
                Vector data(std::istream_iterator<DataType>(inputStream), {});
                
                // Now show result to user
                std::cout << "\nRead values are:\n";
                std::copy(data.begin(), data.end(), std::ostream_iterator<DataType>(std::cout, " "));
                
            }
            else std::cerr << "\nError: Could not open file '" << filename << "' for reading\n\n";
        }
        else std::cerr << "\nError: Problem with filename input\n\n";
        
        // Ask, if the user wants to continue
        bool validInput{false};
        while (not validInput) {
            std::cout << "\n\nDo you want to read more files? Please enter 'y' or 'n'  ";
            if (char selection{}; (std::cin >> selection) && (selection, in{'y','Y','n','N',}) ) {
                validInput = true;
                userWantsToContinue = (selection, in{'y','Y'});
            }
            else {
                std::cout << "\n\nInvalid input, please retry\n\n";
            }
        }
    }
    return 0;
}