Python lacks the tail recursion optimizations common in functional languages like lisp. In Python, recursion is limited to 999 calls (see sys.getrecursionlimit).
If 999 depth is more than you are expecting, check if the implementation lacks a condition that stops recursion, or if this test may be wrong for some cases.
I dare to say that in Python, pure recursive algorithm implementations are not correct/safe. A fib() implementation limited to 999 is not really correct. It is always possible to convert recursive into iterative, and doing so is trivial.
It is not reached often because in many recursive algorithms the depth tend to be logarithmic. If it is not the case with your algorithm and you expect recursion deeper than 999 calls you have two options:
1) You can change the recursion limit with sys.setrecursionlimit(n) until the maximum allowed for your platform:
sys.setrecursionlimit(limit):Set the maximum depth of the Python interpreter stack to limit. This limit prevents infinite recursion from causing an overflow of the C stack and crashing Python.
The highest possible limit is platform-dependent. A user may need to set the limit higher when she has a program that requires deep recursion and a platform that supports a higher limit. This should be done with care, because a too-high limit can lead to a crash.
2) You can try to convert the algorithm from recursive to iterative. If recursion depth is bigger than allowed by your platform, it is the only way to fix the problem. There are step by step instructions on the Internet and it should be a straightforward operation for someone with some CS education. If you are having trouble with that, post a new question so we can help.