The question is pretty much in the title.
My country has a nationalized version of VISA which makes the fees pretty damn low; about 0,4% I think - there might be hidden costs I am not aware of.
Of course on top of this the shops have additional costs per year for their terminals.
The data price for internet traffic is quite low so for a TX at 500 byte it would be around 1/1.000.000*0,18$.
Of course there are other costs, but all in all the BTC network should not cost much to operate technically.
In light of these numbers and to stay competitive even in efficient markets I would program an automatic (1/10.000*transfer amount) for fee into the card chip.
Considering that most transactions today are without a fee, I am thinking that the cards should keep working for quite some time without being ignored.