Often, apps start permanently crashing on boot after update

Starting from a few weeks ago, I'm having a problem where after I update an app, it often becomes permanently broken. It will always crash after booting.

This doesn't seem to have anything to do with the app itself, as I've had the problem with Facebook, Chrome, Soundhound, and 5 or 6 others. It doesn't happen every update, but even occasionally is way too often.

I am able to "fix" the problem by deleting the app and reinstalling it, but that means that I lose all of the data associated with the app. Restarting the phone does nothing.

I have an iPhone 4S with iOS 7.1.2. I've had this phone for more than 3 years now and it only started doing this in the last couple weeks.

If anyone knows why this is occurring, I would love to know. Barring that, if anyone has any tips on how to reinstall an app without losing the data, that would be useful as well. Thanks.