According to this website, in Shrewsbury, MA from December to April it rained about 13" or about a foot. According to this EPA website, normal rain has a pH of around 5.6 (due to carbon dioxide in the atmosphere) while the most acidic acid rain is around 4.3

If your pool has an average depth of 4.5 feet, then one foot of rain would replace 1/4.5 = 22% of your pool water through a process of continuous dilution which is equivalent to a drain/refill of 20%. If you started with a TA of 80 (and a CYA of 30) and a pH of 7.5, then replacing 20% of your pool water with "acid rain" water with a pH of 4.3 means adding 10^(-4.3) moles/liter of hydrogen ion and you would remove up to 20% of the carbonate buffer. So the pool's TA would drop to 64 (due to CYA going to 24) mostly from dilution (not acidity), but the pH would barely drop at all (about 0.02) because even acid rain isn't very acid when added to the pool's "buffered" water.

Rain can certainly cause the TA to go down and the pH to drop, but it would take a lot more rain than one foot. Even replacement of 80% of the water would only have the pH drop down to around 7.2, but after that the pH can drop much more rapidly.

So I still can't explain why you saw such a large drop in TA.

Richard