The routers can NOT run without firmware. It is just like Windows Operating system. No computer can run without an operating system. Computer can have problems with corrupted operating system, same way with router can have problems with corrupted firmware. Believe it or not, every machine, whether it is computer, Router, modem, even on your own pagers, they got their own operating system too.
For me, I had similar problems too, and at first I thought it was routers and I had to investigate only to find out that it is ISP that is causing problems, they have been disconnecting from time to time and I'm pizzed off.