I set up a mail server using a raspberry Pi, last January. I have another server that pings it once per minute, to check that it's still running, and it emails me if it isn't. Another server power-cycles the Pi if it's been non-responsive for a few seconds.
That Pi has now been running non-stop for nine months; I just checked the "uptime" at 263 days.
If anyone thought that the Raspberry Pi wasn't stable enuogh for serious use, they're wrong. You do need a good power supply (I'm using an old PC power supply, with a step-down circuit to get the 12 volts down to 5.3).