We have a new Shower (no tub) that used to work just fine but now, after a few minutes of hot water, the water comes out cold. If we turn on the tub (seperate facet) then the hot water returns.

It could be a bad cartridge in either faucet. Is the tub fuacet a single handle moen too?

Sounds like hot and cold balancer is sticking. Take out cartridge and balancer and shake balancer and see if it rattles to free it.

If it is Moen positemp cartridge open the PDF file below and will show you how to remove, clean and install the cartridge, Thanks.

John