When I purchased this home the TA was testing at 100 and the pH was above the test kit range. It took two gallons of MA to get it down to about 7.5. I discovered shortly after that the pH would bounce right back up to 8.2 after a couple of days. I'd add another gallon of MA to get to 7.5 and repeat the process for a couple of weeks. My TA is now down to 40 and the pH still keeps climbing right back to 8.2 a couple of days after adding MA.
The plaster is about 35 years old, so I don't think it's contributing.