jeffc wrote:

Oil based primer is not necessarily the solution. By "primer", I assume you
mean a stain blocker. You have to know what you're trying to block
(assuming it can't just be washed off first.) As a general rule, use oil
based primers for water based stains, and water based primers for oil based
stains (for fairly obvious reasons - oil and water don't mix and therefore
can't bleed through.)

We should clarify that not all primers are stain blockers - that's not
clear from your post. Knotholes will bleed through either oil or latex
paint or primer. Either oil or latex stain blocking primer will seal
the stain, some better than others, but shellac-based stain blocking
primers work best. You can also use straight shellac prior to regular
primer.

In the OP's situation insufficient preparation is assuredly the
problem. Kitchens, as others have noted, are problem areas to paint.
Years of grease buildup can take a lot of work to remove, and what
looks clean enough after an initial cleaning isn't necessarily clean
enough to paint.

R