By "shallow" rim, do you mean "narrow" rim?

If the tube is not fitting comfortably in the tire and in the rim, a good bump will make it squish between the two and, BANG!, there's your pinch flat. But as bean and thom suggested, the amount of pressure in your tube can also be a factor, as a soft tube will "squish" faster than a properly inflated one will.

What's the manufacturer's suggested psi, and what psi are you running?