IOS and Android (sorry can't help but bring this comparison up) are completely different architectures in terms of programming and design, and as such an iPhone DOES not slow down regardless of what you do with it. Now, of course if your playing a high specced game that your processor cannot handle, your game won't run smooth but the operating system always will remain as so.
Android tends to get slower because of the different ways they handle things, such as multi tasking, they have - what android fans like to tout - 'true' multi tasking and as such programmes tend to stay in full operation even when you are not using them, this causes the phone to become slow and unresponsive and its why google has added a convenient "Close all" button just with a simple swipe. Its also the main reason why their processors are alot more powerful because its needed to run these operation systems smoothly and why iPhones are still using single and duel cores, android however have quad cores and soon hexacores.