I have an aav that is letting water come up and out of it when I drain the sink in my kitchen. When the tap is running with the stopper out this problem does not occur. I tried pouring some drain cleaner down but this does not seem to be the problem. Why would all of the sudden, after living here for 13 years, this happen?

Your AAV has failed and needs to be replaced. Pick one up at your local p-lumbing store and replace it, Good luck. Tom