What kind of AC do you have that would take air from your basement and move it outside?
A central AC wouldn't do that. At most it'll circulate the air in the entire house so if your basement has more CO2 than the rest of the house, having it running would move some of that to other floors.
A central AC with recirculate turned off (so it allows some inside air out and some outside air in) might turn over enough air to cause the pH to swing.
However, I wouldn't be surprised to find out that a window unit or central air vent was blowing on or near the tank and just helping with gas exchange.
Just for kicks, you could try pointing a fan at it for a few days. If the pH goes back up, it would imply there's not enough water to air gas exchange since in that scenario no air from the room is regularly being exchanged with air from other parts of the house or outside.