So wait their god dies? Then that means it is not a god.

The idea that gods are always immortal comes from some specific religions and mythologies. For example, Norse gods are actually supposed to die at Ragnarok, and some Greek gods and Titans also die in certain myths.
A “god” basically just means a being that creates, rules, or has power over nature or human fate. It doesn’t have to be all-powerful, all-knowing, or immortal.