Only recover Tenacity score if the player has an active game
The current Tenacity system recovers the Tenacity at a rate of approximately 0.5% per day. This happens whether or not the player is active. I suggest that, for players with a positive Tenacity, this only occur if the player has an active game with other players (public or private).
Training games and Private games against the AI should not count for this.
One of the main ideas of tenacity recovery over time is that a player who needs to quit and be away from the game for a while for whatever reason can come back at a later date and not be too harshly punished for it. Tenacity is mainly intended to stop serial droppers.
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Whisperer commented
Thanks for the detailed explanation.