Hi @Delia8,
Ref: What is a pre-approval?
Your pre-approval is simply you accepting the booking variables of an enquiry. This allows the potential booking to automatically finalise to a Reservation should the potential Guest complete the necessary steps.
Your pre-approval does not expire at any time, even if the potential Guest books elsewhere. It's good practice as a Host to follow up on the enquiry if you suspect they've gone elsewhere... then you can cancel it off.
A pre-approval does not block out your Calendar so there is no negative impact on other potential enquiries. There have been times where I've informed Guests that I have multiple enquiries and pre-approvals for the same dates and it's a first in, best dressed policy.
I'd suggest it'd be reasonable for Airbnb to cancel any pre-approvals a week after the enquiry has gone quiet. Probably not high on the priority list for Airbnb.
Cheers,
Paul