I know I'm a bit late to this party, but apparently this bug is still present. Just ran into the same thing, very annoying to say the least.
There is a remedy though - if you do not mind rummaging around in your save file a little bit with Notepad++ or something the like. Open the file, find your Keepher character by searching their name. Then a bit further down, just behind their level entry, you'll find a field called "levelUpUnspentPoints" [x]. If value x in that field is anything but 0, your char can't gain abilities. They still collect XP and level, but somehow the reward gets locked out.
I dunno the why's or how's, not really that code-literate, but I've been messing with save files this way since Wasteland 2, and this method works. On next level-up after removing unspent points, it will trigger level-up rewards again as intended. So once you realize itz happening, go do this immediately, otherwise those points pile up and you potentially waste time & effort.
But while you're already in the save file, if you're so inclined, you can make up for wasted time & nerve by finding the "Learned Abilities" field which is right behind the "levelUpUnspentPoints" and just fill in the abilities you want for your keeper^^. Simply the use same name as in-game, just put it in " ", and note it's case sensitive. Or go a little above into the "eroMoves" or "statusEffects" fields and add whatever naughtyness or attributes/traits you want for your Keepher
If you wanna keep it more random, remove a few levels, add a couple dozen Crystal Shards to your stack in the inventory section, craft some XP crystals, use em and see what your Keeper gets (I like save scumming that part until most my chars get "Sexy" & "Likeable", but that's just me^^).
Hope this helps, even belated as it is^^. Happy X-mas, fellow Keephers!
EDIT: Meeh. This apparently works - but only once. After leveling, I found it will revert to the bugged state on next "silent" level-up during shop purchase. Thought I had the solution, but no dice. In any case, the save edits are at least a way to get the stuff one would miss out on, and pick & choose^^.