Did you use a stripper like soygel or citrus on it? If not cleared away, stripper could be attacking the new paint.

No stripper, just light sanding prior to kill

That's kilz

oil based kilz or water based?

Water based

I would sand it off and apply Zinsser's 123, Kilz water based products are known to be problematic.

Sticky primer points to a problem with the preparation of the substrate.
The sanding needs to be progressive enough to break the film/seal created by the stain/varnish finish. Start with #120 grit sanding sponge, progress to a #150 grit, finish with a #180 grit sanding sponge. Or course, medium, fine. Vacuum dust and wipe clean with mineral spirits.

Proceed with primer and two full coats of quality paint.

Thanks all for your comments.
@michael, DH thought it was problem with substrate also.

I am working on two dressers. Both got kilzed. Dresser #1 seem to dry properly and I proceeded to apply one cost of white oil based paint. It looks great.

#2 is the one giving me fits. The dressers are going inside closets, and I didn't want/need to have them perfect. What would happen if I went on to apply oil based paint? Just trying to get away with half ass workmanship if I can, lol

#2. If you apply paint over sticky primer and store it behind closed doors, the off-gassing may add unpleasant odors to your living area.

hmmm. don't want that. thanks I guess I better do it the right way, sigh

Correction: the dresser in question is pine, nothing really valuable. But I decided to start from scratch and strip the entire piece. Which would be the best product to use? Will the citrusgel be good?