Itch doesn't seem to query users' Patreon information at the time of download in some scenarios.
If a game has two pay levels, one at $ and another at $$, Itch will successfully query a user's support tier and grant them access to their paid version of the game. If a user is at $ tier, downloads the game, upgrades their membership to the $$ tier, then goes to download the game again, they won't have access to the $$ version of the game. They'll only see the $ version when they go to download.
This issue also appears to happen when attempting to move from a free tier to a paid tier. While a user's subscription tier will change on Patreon's side, Itch will still only allow access to a free copy of the game.
Revoking a Patreon key permanently revokes access to a user's copy of a game. While this seems to work as intended, there doesn't seem to be a way to "unrevoke" a key. Even if a user is a subscriber, once the key is revoked there's no way for them to regain access even if they have an active subscription.