"Latex is water soluable"

That means paint should be washing off most of the exteriors of homes,
which it obviously isn't. Latex paint is suspended in water in the
can. When applied, the particles bind together, forming a tough
flexible surface that is no longer water soluble. One of the
advantages of latex is that it is more flexible and can allow moisture
in the wood to escape without cracking or peeling.

One key question is how is the stain peeling? Is it only one or both
of the new stain layers that are peeling off? Or is it peeling from
the layers that are now underneath and were there all along? Was it
peeling before being painted? It's possible that the oil layer is
trapping moisture that previous latex stain allowed to escape from the
wood. That wood be my first guess, without knowing more about the
location and application. Another key question is was the surface
properly prepared before applying the stain? Was it washed clean and
any loose material scraped, etc?