I've long been tired of the "Apple better do X quickly or they'll miss the opportunity forever." (see: blu-ray, 3G for the iPhone, etc.)
So I won't go so far as to say, "THEY NEED A BIGGER SCREEN OR THE COMPANY WILL DIE."
But they need to do something. iOS is getting desperately long-in-tooth. Aside from a slightly longer screen, very little has changed about the hardware in 3+ years now. I'm not counting them out, but I starting to get a little antsy.
What do you mean by "Very little has changed about the hardware". Do you mean how it looks? Because Apple is not going to drastically change the looks, they will refine it. They got it right the first time. Perhaps an updated UI with iOS7 this year. And in terms of actual hardware/chips, the A6 and LTE chipset are a huge improvement.