I passively left my power meter plugged in 24/7 while mining because i thought it would be more fun to be able to check it 24/7. Turns out it was a bad idea as this morning i woke up to a blown/melted socket and powermeter. Hopefully my rig isn't damaged.
Another reason to not keep it on 24/7 is for savings. The power meter probably consumes a negligible amount but even at 1 watt per day, that is still money saved looking at the big picture (365 days a year).