Either the locker well is too shallow ( or too full) for the line to lay down or the line is too stiff and the same thing happens, the line 'backs' up in the locker and there isn't enough free fall depth for the line to get pulled down by gravity.
Another possible although less often reason is that the spring loaded arm on the winch is not applying enough pressure to keep the chain and/or rope engaged in the capstan.
I would try the overnight fabric softener treatment first to see if that helps.
As I think I mentioned, if you have a lot of line in the locker, pull it out onto the deck. Now return about 100 feet back into the locker( 100 feet from the anchor back) now try deploying the anchor in about 30 feet of water and retrieve it after setting it. If the line doesn't get kinked and bind, you know that the piling of the line is causing the capstan to jam.
If just paying out some line when it jams and then retrieving it works without you having to go into the locker and flattening out the pile of rope, I would make sure the capstan and rope are a match