My texbook says that proteolysis can occur once in the lifetime of the enzyme? I know that proteases must cleave the zymogen at more or more specific locations, but why can't the process take place more than once?
Because you mention zymogens, I assume the proteolysis you are referring to is the conversion of the inactive to active form of an enzyme by cleavage. The reason this would only happen once is that there isn't any process to put the two cleaved halves of the protein back together, so once cut in half it stays that way until degradation.
The proteolytic enzyme that is doing the cleavage of the zymogen will repeat this process over and over with multiple copies of the zymogen: it is the zymogen itself, the target, for which this is a once-in-a-lifetime event.
It would certainly be possible for a zymogen to require multiple cleavage events, but each of those events could only happen once.