A Sanctuary’s ability is activated for the rest of the game once its Decay counter reaches zero, regardless of its Aegis value. If a Sanctuary is destroyed (Aegis reaches zero), it is removed from the game and cannot be repaired. However, if a Sanctuary’s Aegis is reduced but not to zero (i.e., it is damaged but not destroyed), and then repaired above zero, the Sanctuary remains in play.

If the Decay counter has already reached zero, the Sanctuary’s ability is already activated and remains so for the rest of the game, as stated:

• "If the Decay counter reaches zero, the Sanctuary ability is activated for the rest of the game." (page 20)
• "A Sanctuary’s ability is ignored until the Decay track reaches 0." (page 11)

There is no rule indicating that losing Aegis or being damaged disables an already activated ability. Only destruction (Aegis at zero) removes the Sanctuary from play. Repairing Aegis above zero does not affect the status of the ability if Decay is already at zero.

Summary:
If a Sanctuary’s Decay is at zero, its ability remains active regardless of Aegis changes, as long as the Sanctuary is not destroyed. Repairing Aegis above zero does not reactivate or change the status of the ability—it remains active.

Sources:
Page 11, Page 20

Source: Core Rulebook (pp. 11, 20, 22, 24, 26)