Which mic do you have? I assume the stock one. In the MH-31 pin 6 is +5V, but I don't think that has anything to do with it.
The MH-59 mic (the fancy DTMF one) has a power button which shares a pin on the connector with the FST (fast scan). If you momentarily press the button the radio goes into Fast Scan but if you press and hold the button for about a second the radio turns on or off. Thing is you don't have to have the fancy mic for this to work, it does this on the regular mic, too, even though it's not mentioned as a feature.
My guess is the button in the mic is broken, stuck closed so the radio thinks you are pushing the power button.
It's also possible that pin 1 and 2 are shorted together in the mic, cable or port on the radio. Pin 1 is the FST/Power and pin 2 is ground.
So I'd first check to make sure there are no bent contacts anywhere since that is easy, magnifying lens and a flashlight. Next wiggle the FST button to see if it's stuck pressed. If none of that works it's not difficult to open and clean the MH-31. Could just have junk stuck in there.
Unless there is a bent pin on the radio side connector, I think a new mic would fix it. But I don't think there's anything wrong beyond a dirty button, so not sure you can use it as justification to buy a new mic...