How long does a service provider have to charge for repair or replacement of damaged rental equipment?

This question is very specific to the facts and to the contract. Did the renter purchase insurance at rental? Was insurance included in the rental price? Was the damage covered under the insurance? All these factors come into play. If you paid by credit card, keep checking your statement, because such a bill is likely to show up there. It seems it would reasonable show up within one or two billing cycles. Read the rental contract. I assume you are the renter and that you are afraid to ask the rental company, for fear you may cause them to bill you. Such things can be tricky.