I have a script to handle http requests. I'm trying to think of some of the security issues I might have with it. My biggest concern at the moment is how I can manage multiple requests from the same source over and over. For instance someone trying to shut down my system.
Do I need to be concerned or will Apache handle this issue. If not what is the best approach to take using php?
IMHO security has always to be considered from different viewpoints and at different levels.
From what you've described and what I think you're trying to achieve (Denial Of Service Attack countermesure), tough, it's my belief that your best bet would be that of dealing with requests at a lower level (IE packet filtering) than where apache operates. With PHP alone you can definitely perform other security checks, but most likely not do much (if anything) against a DOS Attack.
Check out the mod_evasive Apache module. Also, the Apache documentation has some good tips.