What kinds of things can cause a power supply to cut out?
The specification for the power supply states that the current limiting is "Automatic current limit/foldback". Foldback current limited supplies can cause problems with non-linear loads, especially those that draw substantially constant current. This is because there can be two or more stable operating points, one with the supply in constant voltage mode and one or more with the supply in current limit mode. A brief current spike could 'knock' the supply from one mode to another.

But this is somewhat speculative since we don't know the design of the power supply nor the IV characteristics of your product. It would however be worth trying a constant current limit supply instead.

This is an example of what can happen