As far as im concerned they stay there forever, but why dont you just add a small step for logging your approval requests in your flow?
You can be very creative and there are a ton of ways to log it, but what about a Teams team, in which the flow sends a message after every approval proccess, in which it writes all the neccessary information, that need to be logged. You can also take the channel email ( every team has a channel email ), and make it send an email there (with the neccessary information as a pdf in the attachment).
Think outside the box and just use a channel or email for loggin purposes, where you send the information at the end of the flow.
I couldn't find any info online about how long the approval proccesses stay logged in there, but as i said, i think you can just find another solution for that, that works even better.
(you can also make it write it in an excel sheet if thats what you're looking for, or make it save the generated pdf in a onedrive folder that you sync with your company internal data structure)
