malloc() returning a null pointer

I'm attempting a C programming assignment where I need to iterate through each index of each line of a document, and set an integer value at each character index in a corresponding array ar:

//Jagged array ar containing pointers to each row
int* ar[line_count];
//The size of each row is the line width * the size of an int ptr
const int line_size = max_width * sizeof(int*);

//For each line
for (i = 0; i < line_count; i++)
{
    //If the first runthrough, copy the blank array 
    if (i == 0)
    {
        ar[i] = malloc(line_size);
        memcpy(ar[i], blank_ar, line_size);
    }
    //Otherwise, copy from the last row
    else
    {
        ar[i] = malloc(line_size);
        //This is set to a null pointer after several runthroughs
        memcpy(ar[i], ar[i - 1], line_size);
    }
    //Edit the current row ar[i]
}

The only problem is, after some 9 iterations, malloc starts returning a null pointer that causes memcpy to (obviously) not work.

Is there any reason this is happening? There is no way I'm running out of memory as I only allocate these tiny arrays 9 times.