After a reboot of OS X, I often need to re-enter my Apple ID password in order to use the apps I bought in the App Store. Sometimes I have to re-enter my password only once and all the apps work (until the next reboot), but often I have to repeat this for every single App Store app I open.
For example, I might get this dialog the first time I launch Reeder after rebooting OS X:

Sign in to use this application on this computer
“Reeder.app” was purchased using App Store on another computer. To install “Reeder.app” on this computer, sign in using the Apple ID and password used to purchase it.
I have tried to delete the following files:
~/Library/Caches/com.apple.appstore~/Library/Caches/com.apple.storeagent~/Library/Cookies/com.apple.appstore.plist~/Library/Preferences/com.apple.appstore.plist~/Library/Preferences/com.apple.storeagent.plist
But this didn't solve the problem. I have reinstalled all the apps, but that didn't help either. Moreover, I have done a clean install of OS X (for another reason) but I still have this issue with Mac App Store apps. Could this be related to my hardware or Apple ID?
Is there anyone who has had a similar problem or someone who might help me?