Frequent iPod touch crashed on 4th generation iPod touch

I've tried searching the forum and couldn't find anybody else who is having this problem, but I thought I would throw out the question, just in case.

Usually an app will start, and then crash after running for several seconds. This happens with Apple apps (like safari, settings, photo, etc.) as well as apps purchased from the app store.

The first thing I do is close the programs running in the background and try to run the app again. This has almost never stopped the crashing.

The next thing I usually do I is restart the iPod. This also does not seem to help.

I have also tried syncing the iPod, and restoring it to factory settings in iTunes. This has also not helped.

I am really at a loss of how to fix the issue. Recently the iPod has not just been crashing to the home screen, but also crashes to the boot screen where only the apple logo is displayed for (what seems like) several minutes.

I have the most recent iPod OS installed and the most recent version of iTunes.

Any suggestions?

tl;dr - My iPod touch is crashing, and none of the basic fixes seem to be working.