H.H.
I had the SAME exact experience with my 2 year old. (He is 2 1/2 now but at 2 we took it away and said it was "all gone" bc he understood that term, (after I found out he was not using it at daycare either, and we were only using it for sleeping) He asked for it a few times here and there for 2 or 3 days, we just said it was all gone and that was it and he stopped asking. Amazingly we also have a 1 year old who was sucking on one right next to him but we just said it was not his, his was all gone and that was the baby's and he was OK with that. (Now at 2 1/2 he has adopted a spiderman blanket to sleep with but he does not carry it around otherwise.)
hope this helps! I work full time too and my boys are 31 mo and 17 mo! so it is pretty nutty over here too! :)