To answer your original question... yes, they can die slowly.
I had a Linksys router doing very simple routing of all incoming port 25 traffic. One day I noticed that a few emails were not being delivered... the next day, a few more... after about a week.. I noticed that about every 10th email was being "dropped". I did a hard reset, and it worked fine for an hour.. then started dropping emails again. I replaced it with a netgear, and the problem was no longer there.