Stalls during idle

Hey, could anyone possibly help?
My boyfriend has a 2003 A4 1.8T Quattro. Every
since he got it, he has been having issues with it.
The check engine light was on from the beginning,
and when he would read the code it would say
catalyst below threshold. He replaced the coil
packs, the spark plugs, the timing belt, oil pan, and
got a brand new exhaust with the cat. It ran great
for about a week, and then threw another check
engine light, that read catalyst below threshold. We
took it to an Audi dealer to have them run
diagnostic testing to see if they could find
something that was wrong. They ended up
replacing a sensor (I'm not sure which one) and it
ran like a champ for 3-4 days. Now, the check
engine light is on again. Every time the check
engine light comes on, it will start fine and then after
a max of 5 minutes of idling to warm it up, it will
stall. It loses rpms at first, but it will recover itself so
to speak, but it will eventually stall. It has also
stalled multiple times while driving. We just want
answers, we don't know what to do. The whole
underside of the car is basically brand new..
Thanks for any help in advance!