Have you tried playing wirelessly in a different location, in case there is interference causing the disconnections?
Have you tried playing online multiplayer on the Switch, if possible?
Have either of you tried playing local wireless with anyone else?
Have you tried hosting/joining an Arena match? One or two matches should be long enough to see if you get disconnected (20 minutes would imply the issue doesn't happen in Arena mode, or is at least significantly less frequent).
If you each start the game from a different user account, if available, does this happen in a new game? That would also require playing up to about 20 minutes, though.
Try clearing the system cache: in the Home menu open System Settings, then select System, Formatting Options, Clear Cache and then the current user.
Note that this will also reset the system language and brightness setting.
Does it make a difference if the host Switch is docked or not, if you can check?