Heatbed shuts down - sometimes

I've just completed the construction of a Mendelmax from a kit. I've got just about everything working now except for one thing. If I try to heat the heatbed up to 110 C it shuts off before ever reaching that temperature (the LED on the board goes out and there is no voltage present at the D8 terminal). All the other electronics remain powered (e.g. there is still power getting to all the stepper motors and the nozzle.) I have managed to get the heatbed hot enough to run several prints using PLA, and I've also managed to get close to ABS temperature by incrementing the set temperature one degree at a time, but if I set it at 110 C and leave it alone, it stops heating when it hits about 70 C. If I wait a couple of seconds and drop the set temperature 10 or 20 degrees, it will usually come back on, but it never makes it all the way to 110 C without shutting off.

I have a 30 amp OEM power supply that came with the kit and a RAMPS 1.4.

Any thoughts as to what is going wrong? Is it my power supply? MOSFET on the RAMPS board?

Any suggestions would be greatly appreciated.