The problem is that when j = ncol - 1, trying to access x(i, j+1) in the line
total += x(i, j+1);
is the same as trying to access x(i, ncol), and you are out of bounds. If I understand your problem correctly, you can just change j+1 to j, assuming y is passed correctly. So, we could change your code to the following:
#include <Rcpp.h>
// [[Rcpp::export]]
Rcpp::NumericVector PVCalc_cpp(const Rcpp::NumericMatrix& x, int y) {  
    int nrow = x.nrow(), ncol = x.ncol();
    Rcpp::NumericVector out(nrow);
    double total = 0;
    for (int i = 0; i < nrow; i++) {
        total = 0;
        for (int j = y; j < ncol; j++){
            total += x(i, j);
        }
        /* The following will always be equal to total but rounded;
           to type less R code for the R comparison,
           I omit the rounding here.
           Notice also the use of [] access operator instead of ();
           this is more efficient.
         */
        // out[i] = floor((100. * total)+.5)/100;
        out[i] = total;
    }
    return out;
}
We can then verify that this both works, and is faster than rowSums():
## Load required packages
library(Rcpp)
library(microbenchmark)
## Source C++ code
sourceCpp("so.cpp")
## Generate example data
x <- matrix(1:9, nrow = 3)
x
     [,1] [,2] [,3]
[1,]    1    4    7
[2,]    2    5    8
[3,]    3    6    9
## Check results are the same
rowSums(x[ , -1])
[1] 11 13 15
PVCalc_cpp(x, 1)
[1] 11 13 15
## Benchmark small example
library(microbenchmark)
microbenchmark(base = rowSums(x[ , -1]),
               rcpp = PVCalc_cpp(x, 1))
Unit: microseconds
 expr   min     lq     mean median    uq      max neval
 base 5.591 5.9210  8.61073  6.475 6.786  137.125   100
 rcpp 2.337 2.5795 19.90118  3.035 3.222 1651.094   100
## Check larger example
set.seed(123)
x <- matrix(rnorm(1e6), nrow = 1e3)
y <- sample(seq_len(ncol(x)), size = 1)
all.equal(rowSums(x[ , -(1:y)]), PVCalc_cpp(x, y))
[1] TRUE
microbenchmark(base = rowSums(x[ , -(1:y)]),
               rcpp = PVCalc_cpp(x, y))
Unit: milliseconds
 expr      min       lq     mean   median       uq       max neval
 base 5.377342 6.052347 6.954338 6.482907 7.834190 11.580706   100
 rcpp 1.447596 1.909504 2.085185 2.023343 2.158256  3.159366   100