Niantic updates official Gift Exchange Known Issues support page for Pokémon GO with multiple issues that it’s now investigating as of February 20

Mateo does not always appear at Gyms.

Issue description: When approaching a Gym at the end of a Route, Mateo does not always appear. Tapping on the Gym will prompt Mateo to appear for a Gift Exchange.

Issue status: Investigating

Having the maximum amount of Pokémon in storage blocks Trainers from completing a Gift Exchange.

Issue description: Trainers who have reached their maximum number of Pokémon are blocked from completing a Gift Exchange. In the meantime increasing the number of Pokémon you can hold or sending one to Professor Willow will allow you to proceed.

Issue status: Investigating

Some Gifts do not appear when tapping on Mateo a second time.

Issue description: After entering, then exiting, and then re-entering the Gift Exchange dialogue with Mateo nearby Gifts no longer appear on the Gift menu.

Issue status: Investigating

Quitting a Route may prevent Mateo from appearing
Issue description: Quitting a Route without finishing it may prevent Mateo from appearing in subsequent Routes, even if you didn’t encounter him before quitting.
Issue status: Investigating