How long are capers good for in the fridge once you open them?

They last forever..

Something close to "forever" if covered with brine. Even using only a small amount at a time, I always manage to use mine up before they go bad.

Brined capers last a long time, but I suggest going to salt packed capers which taste better and seem to last for eternity unrefrigerated. Although do go through them pretty fast. You do have to rinse the salt off before using. The brand I reach for is Rustichella d'Abruzzo, the same company that makes exquisite dried pastas.

I have had them in my fridg for over a yr. submerged in brine they should last for a long time

If they're still submerged they should be good. Taste them. I tossed some recently because they had picked up some off flavors--but there was very little brine in there.

Next year? They're pickled in brine, so like preserved lemons, etc. They're good for a long, long time.
Especially in the 'fridge. Keep it and use it, may I suggest using it for tuna salad, canned salmon salad, or using it for fish fried in a touch of flour, lemon juice, removed. and then deglaze the pan with more lemon juice and the caper and soft butter to make a sauce?