If the stain is still tacky 12 hours after applying it, it will not eventually dry. Stain penetrates wood but if it can't due to excess stain or dirt, it will sit on top without drying. You will either have to sand it or apply another coat of stain to loosen it and wipe it off.

What do you do if your gel stain won't dry?

You're going to have to strip the gel stain off in that area at least. It will eventually dry however when you finish over it the finish will eventually peal off. Personally I would strip it all off and start over. The doors may have at some time or another been waxed or it may be cooking oils or even hand oils.

What do you do if gel stain is tacky?

Allow the wood to dry completely, sand the piece down to bare wood, and apply a coat or two of stain, wiping off any excess. If you applied the stain correctly, and it still remained tacky, it could be due to rainy weather or high humidity. Give it a few more days to see if it improves.