The amount in your Euro savings account will not decline provied you live and spend it in this country however the value of the Euros or purchasing power can decline if we see inflation but that is always a risk, in my view your Euro will buy you more goods in a recession however if we see hyper inflation which is a possibility if the IMF actually step in then all bets are off and your deposit rate should rise.
You will see on other posts that deposits are being moved to other Euro countries that are seen as more stable, people do so to cover a risk of us being booted out of the Euro and having a devaluation of Euro deposits held here in IRL, personally I think this is unlikely but you cannot argue with the sense behind it.