The hard-restart is good advice.
If that doesn't work, use iTunes to restore the phone as new (not from backup), then pipe your songs, apps and other content back onto the phone. It's a bit of a hassle but is the best way to ensure that any software corruption is rectified.
Smartphones are enormously complicated computers, and there's a lot that can go wrong with their software. It's actually rather amazing that they work as well and as reliably as they do, considering how much functionality is crammed inside them-- far more than exists in a PC or Mac.
So, regardless of whether you're running iOS or have stomped in a huff into the world of Android or Windows Phone, you'll very possibly run into the issue of odd behavior here or there, and the solution is always the same: wipe the thing and reinstall everything from scratch.
It's good default advice for fixing odd behaviors in personal computers, too.
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That fixed it, however the problem is back. So I guess I just need to reboot my phone once an hour or so
Sounds like the restore-as-new is needed. That is the first thing the Genius Bar will tell you to do, especially in a case like this when the issue is clearly software-related. (But it's always the first step they'll insist-on even in the case of a seeming hardware failure, like an intermittent home button. The reason is that the button merely triggers software, so any issue could be software as much as hardware.)
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Why not call Apple or take it to the Apple store?
Go ahead, but the first thing they'll insist you do is a restore-as-new. That fixes the majority of issues.