I'm using the ethernet shield to get a large amount of data (around 200 entries) from my server.
That you would then like to store in read-only memory. Nope. It doesn't work that way.
const char *stars[0] = { };
The value in the [] is the number of elements in the array. 0? How useful is that?
So after around 35-ish objects, my data starts to corrupt. So I'm guessing I'm running out of memory.
No. You were stomping all over memory you don't own when the first character arrives. You are not out of memory. You are out of bounds.