As I learn more about the electrical systems on these ebikes, I'm finding the BMS units to be interesting. How many "types" or designs of BMS units are there? I'm getting the impression they are not all created equal in how they read and respond to varying conditions. Of course all seem to have a low voltage protection limit, and it seems all have some kind of high temp cutoff and max charge voltage.
However, there seems to be some variance on other scenarios where some BMS setups trip or don't trip over certain conditions. In the case of the OP's situation here, does the BMS see/read that drop from 53.5 to 48 as a problem requiring shutoff as some kind of safety feature, even though that specific incident probably wouldn't necessarily be a safety issue for the battery? And what determines how the BMS would trip back on after this event?...time?...other inputs by the user such as turning the system back on?...charger input?...something else?
When I see advice given about problems that appear to be BMS related, this is where it seems the "fixes" are different to get the BMS to respond. Am I wrong on my observation, and all BMS units actually have the same internal design and programming? If they are different, I wonder why batteries don't come with a clear data sheet showing what all the parameters of the given BMS actually are along with instructions as to what the user can do to restart...if possible...test, or comprehend what parameters and values exist in the BMS. On the battery for my Bafang BBSHD mountain bike application, I had to call back to the battery builder to find out what the low voltage cutoff in the BMS was so I could make sure my programming in the controller matched the BMS in the battery.
Now, aside from the BMS issue, OP do you have any brake or shift sensors in your application? I had a right brake sensor malfunction that didn't throw a display warning. Motor would cut off much like yours and then start working again for no apparent reason but still no display warning like usually occurs in my 500C Bafang display. I disconnected the brake sensors one at a time and found the problem...no more issue. You don't mention what this motor is on, but if you do have any brake or shift sensors, unplug them to eliminate the obvious.
Also, if I understand correctly, you can unplug your display, plug in the $20 Bafang programming cable, and the motor will run on throttle. It does on mine, and this is one of the elimination tests I did before finding the brake sensor issue. If the program cable lets you operate the bike or whatever without turning off like it has been doing, at least you've eliminated some possibilities.
However, it does indeed sound like a battery issue as diagnosed by others already because that voltage drop isn't right. However, I would ask if your observation of the voltage drop was performed via a multimeter or just watching the display readout. If only on the display, is there a possibility the display is faulty?...I'm just spitballing on that one. Testing with another battery would be very telling and probably reveal it is the battery. However, if you have access to a program cable, that is a quick and dirty test of the display's integrity.