I would get the potatoes out of the ground and into storage the first week they do not increase significantly in size.

Frost would not affect the tubers unless they literally show at the surface.

Have the current plants gone through a bloom cycle?

Some of the plants are blooming right now...I noticed the first bloom a few weeks ago. I haven't noticed a change in the size of the plants in a couple weeks but I haven't been paying much attention to them either.

actually it looks like they are done blooming and some of them are growing little berries.

I was referring to the size of the tubers.

Potatoes are not normally a crop that is replanted for two harvests in one growing season, but you have done so with some success. We dug ours in August from a late April start.

Perhaps you are growing the thin-skinned types that develop more quickly than "baker" types that require three full months to size up.

If the soil at tuber level is merely damp and still crumbles in hand, that is fine. If the soil becomes mucky, that is bad for the tubers. You could put sheet of something over the plants and deflect rain, but I suspect there is not enough warmth or daylight to promote much more tuber growth.