Secondly, protocol wise i can also understand.
Airprint is done via Bonjour, a multicast DNS service. When the printer wlan nic is asleep, it doesn't send multicast packets. This may be the reason that it disappears after being there for a while.
Easy to check i guess: send a print job to the printer to make it active, and at the same time check airprint printer availability on the ipad.
Anyway, my two cents.
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