Based on the behaviour exhibited, my guess is that one, or more, cells in this pack have been "stressed", and have lost about 10% of their capacity. More importantly, the "C" rating has also been reduced to the point that the voltage is sagging badly under moderate loads. The is tripping the LVC circuit in the BMS.
Another point is that if you have two BMS units, one in each pack, the 55V limit is not a problem. Since the packs are in series, the limit is really 110V In any case, it sounds to me like at least the LVC portion of the BMS is working fine, as it is pulling the plug, so-to-speak, before anymore damage can be done. I'm guessing if it does have some sort of voltage clamp/regulator on each cell, it is also working properly. the fact is if you have stressed cells, the voltage will drop about 5% within minutes of eing off the charger.
I'm pretty certain the cells in these are in the prismatic format, where each is enclosed in a sealed bag. With early version of RC LiPo cells using this format, there were a number of quality control issues where tiny bits of moisture got into the bags during the manufacturing process. This usually happened more often if the cells were made in the summer months, when the humidity was higher. What would happen is that at some point in the future, usually within six months, the moisture interaction in the cell would cause it to "puff", When this happens, the cell is pretty much dead.
I think what has happened here is simply that at least one cell was weaker than the rest, and the load just caused it to get damaged/stressed. If you end up keeping the packs, you'll need to do what has been suggested here, and let Steve, or somebody open this pack up in order check the health of the individual cells.
-- Gary