itoa base function in C
Input checking

If the caller passes in a base greater than 17, you will read past the end of rep.
If the caller passes in a base of 0, you will divide by zero.
If the caller passes in a base of 1, your code will infinite loop.
If the caller passes in a negative value but the base is not 10, you will read past the front of rep because your modulus will be negative.  You should always make value positive before proceeding with your loop.

Insufficient buffer size
On a system with 64-bit ints and a base of 2, you will need a buffer of size 65 instead of 50.  (Or 66 if you allow negative values for all bases).
Code simplification
This code:

if (value == 0)
    *--ptr = rep[value % base];
while (value != 0)
{
    *--ptr = rep[value % base];
    value /= base;
}


could be simplified to:
do {
    *--ptr = rep[value % base];
    value /= base;
} while (value != 0);

I'm not sure from your question whether you were allowed to use a do loop or not.  Also, your question says you are supposed to return an allocated buffer but you intentionally didn't, so I'm not sure how to review that part of it.