My house was built in 1903 and the woodwork on the first floor and the main areas of the second floor is beautiful oak. The kitchen, however, is soft beat up wood (I think pine). At some point someone stripped the woodwork in the kitchen and was a bit overzealous in the process and the wood was really chewed up. So, while generally opposed to painting woodwork, I have filled in the worst areas with wood putty and am painting it white (probably what it was in the first place). However, the wood keeps bleeding through the paint. I have primed the wood with Kilz and it even bleeds through this. In some areas I primed with Kilz, then painted with paint with primer in it and then Kilz again. So far so good with that, but why is the wood bleeding through the paint? It doesn't appear to be stained, but I guess I could be wrong. Any suggestions?
Is it knots that are bleeding through, or something else? Maybe posting a picture would help. As a first move, I would consider switching stain blockers from Kilz to Zinsser. The original Zinsser primer that is shellac based, not the new water based one. I have used the water based Kilz and Zinsser for mold bleed through control, with pretty good results, but shellac based primers like the original Zinsser are especially good sealants and are simply the best for certain projects. You will know it is the right one if the instructions involve clean up with denatured alcohol instead of water. That might allow a single primer coat. Others may have different strategies.