Why does my sidecar disconnect repeatedly when I connect my iPad Pro (OS15.3.1) to MacBook Pro (13in, M1, 2020; Monterey 12.1) ?

Redefine iPad setting. Use Settings -> General -> Reset -> Reset all settings.

You don't loose data but you have to reconnect to your wi-fi (same Network for the Mac) .

It works for me

I have MacBook Pro (13-inch, 2016, Four Thunderbolt 3 Ports) and an iPad Air 3rd generation.

Wirelessly, or via USB?

If you already tried (to no avail) ALL the steps provided in this support article (even the section "Change settings"):--> Use an iPad as a second display for a Mac - Apple Support, I suggest that you contact Apple Support directly, using this link:--> Get Support

Regards

Giulio