I think age and paint might be holding it in place. Try working it off with a putty knife.
I was having problems removing these covers, too (beyond age and paint). After damaging some window trim trying to get them off, I check around the internet and learned something helpful (that I should have noticed myself).
There is a small ridge inside the top of the covers, that fits into a little grove on the mechanism. So trying to pull/pop them off from either side of the top of the cover didn't work very well. For me, the trick was to work on popping them up & off from the top, directly behind the hole area for the crank (to pop that little ridge up and out of the groove). I used a small, 1 inch scraper that was a little flexible. Hope this helps.
THANK YOU for pointing out this ridge!! I was on the verge of just breaking the damn thing off.
I also thank you for pointing out this ridge. It's virtually impossible to remove without denting the wood when using a small screwdriver, so I'll also be removing the ridge for easier future removal. THANKS
This was a great post. I realized there must have been something else holding the cover in place but hated to ruin a molding to find out. I used a paint can pry tool that paint stores give away. It is thin and has a curved lip which worked well. Thanks again. John
https://www.youtube.com/watch?v=b7338Y-I3IA