You are specifying all the red elements into the fifth row by using grid-row-start: 5. Yes, the red elements are placed to the fifth row, and that is not immediately visible as you haven't specified an explicit row definition (say using grid-template-rows).
Implicit Rows
You can define the implicit row definition using something like grid-auto-rows: 50px and see that the red element are actually in the fifth row: 
ul {
  display: grid;
  grid-template-columns: 1fr 1fr 1fr;
  grid-auto-rows: 50px; /* specify row height */
  list-style: none; /* remove bullets */
  padding: 0; /* remove default ul padding */
}
.blue {
  background-color: blue;
}
.red {
  background-color: red;
  grid-row-start: 5;
}
li {
  border: 1px solid #bbb; /* border for illustration */
}
<ul>
  <li class="blue">
    <h2>1</h2>
  </li>
  <li class="red">
    <h2>2</h2>
  </li>
  <li class="blue">
    <h2>3</h2>
  </li>
  <li class="blue">
    <h2>4</h2>
  </li>
  <li class="red">
    <h2>5</h2>
  </li>
  <li class="red">
    <h2>6</h2>
  </li>
  <!-- If you delete this (or any other "red") "li" element then it's working fine -->
  <li class="red">
    <h2>7</h2>
  </li>
  <li class="blue">
    <h2>8</h2>
  </li>
</ul>
 
 
Implicit Columns
Now your question is why the fourth red item is in the same row - because you have placed all of them in the same fifth row. An implicit grid column is created with auto width - you can control this width using grid-auto-columns:
ul {
  display: grid;
  grid-template-columns: 1fr 1fr 1fr;
  grid-auto-rows: 50px; /* specify row height */
  grid-auto-columns: 100px; /* specify column width */
  list-style: none; /* remove bullets */
  padding: 0; /* remove default ul padding */
}
.blue {
  background-color: blue;
}
.red {
  background-color: red;
  grid-row-start: 5;
}
li {
  border: 1px solid #bbb; /* border for illustration */
}
<ul>
  <li class="blue">
    <h2>1</h2>
  </li>
  <li class="red">
    <h2>2</h2>
  </li>
  <li class="blue">
    <h2>3</h2>
  </li>
  <li class="blue">
    <h2>4</h2>
  </li>
  <li class="red">
    <h2>5</h2>
  </li>
  <li class="red">
    <h2>6</h2>
  </li>
  <!-- If you delete this (or any other "red") "li" element then it's working fine -->
  <li class="red">
    <h2>7</h2>
  </li>
  <li class="blue">
    <h2>8</h2>
  </li>
</ul>
 
 
Solution
You can do this to group them:
- set - order: 1to the red items so that they always come after the blue ones,
 
- set the first - redelement to the first column using- grid-column: 1and the rest will be auto-placed using- grid-column: auto.
 
See demo below:
ul {
  display: grid;
  grid-template-columns: 1fr 1fr 1fr;
  list-style: none; /* remove bullets */
  padding: 0; /* remove default ul padding */
}
.blue {
  background-color: blue;
}
.red {
  background-color: red;
  order: 1; /* red items have higher order */
}
.red { /* first red element into first column */
  grid-column: 1;
}
.red ~ .red { /* subsequent red elements auto-placed */
  grid-column: auto;
}
li {
  border: 1px solid #bbb; /* border for illustration */
}
<ul>
  <li class="blue">
    <h2>1</h2>
  </li>
  <li class="red">
    <h2>2</h2>
  </li>
  <li class="blue">
    <h2>3</h2>
  </li>
  <li class="blue">
    <h2>4</h2>
  </li>
  <li class="red">
    <h2>5</h2>
  </li>
  <li class="red">
    <h2>6</h2>
  </li>
  <!-- If you delete this (or any other "red") "li" element then it's working fine -->
  <li class="red">
    <h2>7</h2>
  </li>
  <li class="blue">
    <h2>8</h2>
  </li>
</ul>
 
 
Explicit vs Implicit Grid
Explicit grid
Explicit grid is the grid that you define using grid-template-columns, grid-template-rows, grid-template-areas and related shorthand properties - see excerpts below from W3C:
Explicit Grid (W3C)
The three properties grid-template-rows, grid-template-columns, and
  grid-template-areas together define the explicit grid of a grid
  container. The final grid may end up larger due to grid items placed
  outside the explicit grid; in this case implicit tracks will be
  created, these implicit tracks will be sized by the grid-auto-rows and
  grid-auto-columns properties.
See an example below of and explicit 2x2 grid which we will come back to shortly:
.wrapper {
  display: grid;
  grid-template-columns: 100px 100px;
  grid-template-rows: 50px 50px;
  grid-gap: 5px;
}
/* styles */
.wrapper > div { border: 1px solid cadetblue; background: lightblue; display: flex; justify-content: center; align-items: center;}
<div class="wrapper">
  <div>1</div><div>2</div><div>3</div><div>4</div>
</div>
 
 
Implicit grid
If you have more content or elements inside the grid container but outside the explicit grid definition, then that is part of what is called as the implicit grid. 
You control the size of your implicit grid using grid-auto-rows and grid-auto-columns properties.
Implicit Grid (W3C)
The grid-template-rows, grid-template-columns, and grid-template-areas
  properties define a fixed number of tracks that form the explicit
  grid. When grid items are positioned outside of these bounds, the grid
  container generates implicit grid tracks by adding implicit grid lines
  to the grid. These lines together with the explicit grid form the
  implicit grid. The grid-auto-rows and grid-auto-columns properties
  size these implicit grid tracks.
You can see implicit rows created if you have more grid items in the example above - these rows can be sized using grid-auto-rows property:
.wrapper {
  display: grid;
  grid-template-columns: 100px 100px;
  grid-template-rows: 50px 50px;
  grid-gap: 5px;
  grid-auto-rows: 25px; /* size of implicit rows */
}
/* styles */
.wrapper > div { border: 1px solid cadetblue; background: lightblue; display: flex; justify-content: center; align-items: center;}
<div class="wrapper">
  <div>1</div><div>2</div><div>3</div><div>4</div>
  <div>5</div><div>6</div><div>7</div><div>8</div>
</div>
 
 
To have a look at implicit columns created you can try placing some grid items beyond the second column - these rows can be sized using grid-auto-columns property. See how a new column is created and how the grid behaves:
.wrapper {
  display: grid;
  grid-template-columns: 100px 100px;
  grid-template-rows: 50px 50px;
  grid-gap: 5px;
  grid-auto-rows: 25px; /* size of implicit rows */
  grid-auto-columns: 25px; /* size of implicit columns */
}
div:nth-child(5), div:nth-child(6) {
  grid-column: 3; /* place in thrid column */
}
/* styles */
.wrapper > div { border: 1px solid cadetblue; background: lightblue; display: flex; justify-content: center; align-items: center;}
<div class="wrapper">
  <div>1</div><div>2</div><div>3</div><div>4</div>
  <div>5</div><div>6</div><div>7</div><div>8</div>
</div>