TA is a source of rising pH in its own right. A higher TA means there is more over-carbonation of the pool water and when that carbon dioxide outgasses from the pool, the pH rises. In your case with a pool cover, this effect is almost eliminated so you may not find that the pH rises at high TA levels.

A higher TA also buffers the pH more which means for the same acid or base getting added to the water, the pH change is less. Between this effect and the carbon dioxide outgassing effect described above, the latter is normally more dominant at high TA levels. In your case, with a pool cover, the former effect is the dominant one so a higher TA should have your pH move less. However, when you have to adjust the pH back to "normal", you will still need to add as much acid or base to compensate. That is, a higher TA reduces the rate of pH change, but does not change the amount of acid or base needed to bring the pH back to where you want.

Your significant pH drop is still a mystery, however. Something acidic is getting into your pool (or an acidic chemical process is occurring) and I don't know what that is. When chlorine gets used up, the pH will drop, but I assume you didn't close your pool by adding a lot of chlorine and lowering the pH at that time (normally you just let the pH go up when chlorine gets added).

Richard