What are some limitations imposed by a fixed array size?

The most reasonable assumption I can make is that you are referring to the data structures used when programming - some specification is, perhaps, in order.

In such case, the name itself says what - fixed arrays cannot accomodate a growing numbers of values beyond their initial limitations. Though I'm highly inexperience in programming, I can't imagine that, without context, any more definite answer can be given...

But hey, if anyone disagrees with me, don't take my Word.