It has to do with where Google Play installed the app. This support note is from Swiftkey, but I think it is the same concept with all keyboard app downloaded from Google Play.

After Jelly Bean update, Swiftkey keeps returning to android default keyboard after restart or shutdown

 

There is an unconfirmed fix for this, but try at your own risk. Because the problem happens only if you download from Google Play store. You could find a backup program to back up your keyboard. Once it is backup, delete it from your phone, and restore it from your backup. Some people said that works for them.

 

People using swift key 3 are also having this problem and still no word on a fix as it's on Google side apparently

 

Funny, I have no such issue even with different roms. :what:

 

I am using Kii keyboard. It's great. You can use split screen, (portrait and landscape) adjust the spacing of the keys, key rows, size of keys, and adjust the keyboard padding left and right. I broke my left wrist last year and it's weaker, so I moved the left side in more, and the right just a little. You can download other keyboard skins and themes. Best of all I have rebooted, done a battery pull, and it still defaults back to Kii. Volume Locker and Kii are the best apps since sliced bread!!

 

Same thing happens to me with SwiftKey after reboot. I've learned to deal, & onlyreboot maybe twice a week anyway. Going out of my way to use something other than the stock keyboard is perfectly fine with me

Hope to see a fix later on though.