I've found they keep virtually forever (or until you eat them all up, which around here, is pdq)!

Have kept In oil for over 6 months, with no adverse problems

Also- once the anchovies are finished (which never seem to last longer than a week in my home) we use the olive oil that's left drizzled over homemade pizza, or in the base of tomato sauce!

As long is there is sufficient salt covering the fish, they should last a long time. If you can see some bits above the salt line consider adding some oil or kosher salt. Salting is one of the oldest forms of preserving food and is time tested.

Also perhaps add more salt. If you can find the tin packed anchovies in salt, those are really good too. They are a bit more high maintenance in use but they have a longer life. Anchovies rock!!

I manage a few weeks, but longer if you top-up the oil. Otherise, the bits that are not in oil start to discoulour. Still OK, but not as pretty.