How long does a model rocket motor last?

Provided they are kept in a dry, cool, and stable environment, they should last indefinitely. The ingredients are non-volatile, so they do not really degrade over time.

If you want to know how long they burn for, you need to look at the rating on the side of the rocket. A higher thrust number means that it will burn for a shorter amount of time. Most small model rocket engines burn for 3 to 5 seconds.