With the high vacuum of the moon, an area shielded from the sun will be heated by solar energy only by conduction through the rocks, which would be very inefficient over a long distance. It will equilibrate with space by radiation, which gets inefficient as the temperature drops. At some point you'll reach a steady state, where the heat arriving equals the heat being lost, and the steady state will likely be very cold. The vapor pressure of ice goes almost to zero at -100 C, and as importantly the rate of sublimation is almost zero. So ice in a crater could potentially last a long time. In principle, you're right; at equilibrium, it would all sublime away. However, calculating how long that might take involves so many very loose estimates that I'm sure people could come up with scientifically justifiable estimates that differed by orders of magnitude
Why so loose? Do the math and get the upper and lower limits, and we'll see if they fit into lifetime estimates of the Earth/Moon system.