iPad printer goes in and out when finding printer

You may find that restart of your network components will resolve the problem. You’ll need to restart your network devices in the correct order. Assuming that you WiFi Router provides DNS services for your network, restart devices in this order - allowing time for devices to fully boot/restart prior to restarting other devices:

• WiFi Router
• Upstream wired Network Switch(es)
• WiFi Access Points / Network Extenders
• Other fixed infrastructure devices - such as Printers
• Client devices

Restarting your iPad, after restarting other devices in the correct sequence, is most simply achieved by a forced-restart of the iPad:

• On an iPad with a Home button: Press and hold the top button and the Home button at the same time. When the Apple logo appears, release both buttons.
• On an iPad with Face ID: Press and quickly release the volume up button, press and quickly release the volume down button, then press and hold the top button. When the Apple logo appears, release the button.

If you continue to have difficulties, check to see if your iPad is using the new WiFi Private Address feature. This feature is intended to provide additional privacy and security when using “public” (untrusted) WiFi networks.

Settings > WiFi > [Your WiFi Network / SSID] - tap the “i” icon - Private Address

The Private Address feature is largely unnecessary for your home WiFi network; if enabled, Private Addressing can interfere with anticipated operation of other devices, such as AirPrint. In such circumstances, you may need to disable this feature - and can be enabled or disabled for each individual network.

Use private Wi-Fi addresses in iOS 14, iPadOS 14, and watchOS 7 - Apple Support

The fifth bullet-point refers to a restart of client devices (i.e., plural). My apologies if this was not sufficiently clear.

It is nonetheless good to learn that the problem is now resolved.

You are very welcome.