My significant-other paints professionally and she's seen bleed-through
of *something* through the walls a number of times. Cleaning the walls
thoroughly before painting is necessary but isn't always sufficient.
If memory serves, she does use an oil-based primer in such cases----and
THAT isn't always sufficient. Though it usually works if enough coats
are applied.
Kitchens are often a problem area for painters because the oil mist
generated during years of cooking soaks into the walls.
Good luck! -- Terry
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.)
The brand is not important, the function and type is important.
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