Hi Don,
I seem to recall that
some Hailong batteries needed to have the power switch in the On position while charging for the battery to be fully charged and the cells balanced.
It might be worth trying this on your battery to see if it makes any difference to the fully charged battery voltage.
Did you also charge it fully using the battery's original charger, and continue to charge it for several hours after the green LED had come on the last time you charged it?
When you next charge your battery, check that the battery voltage is going all the way to ~58.8V, and make a note of the battery voltage before you start your ride to see how much it has dropped since the charger was removed. My 48V battery will typically only drop 0.1V
(from 54.54V to 54.44V) when it has just been standing for a few hours after a full charge.
It might also be worth visually checking the condition of the connector pins where the battery fits into the battery cradle for signs of burning/arcing, along with any other battery cable connections, as a poor connection/battery contact could also cause similar cutting out problems.
My lowest observed voltage on my 48V 13S Hailong battery was 37.91V when I initially checked its capacity by performing a full discharge until the
BMS cut the power, and the stated cut off voltage was 36.4V
(2.8v/cell). So I would expect your battery voltage to drop down to 41V before it cuts out if all the cells were still nicely balanced and in good condition.
My Hailong battery that I regularly use still has a lot more capacity than it did when I first received it over three years ago.
I purchased the 48V 20Ah battery from a seller on AliExpress, but the maximum capacity measured after the first few charge/discharge cycles was only just over 7Ah!
(just 35% of its stated capacity).
As the battery was clearly not as described, I messaged the seller, who said my measuring method was not accurate and I should use a professional measuring instrument
(even though the 2 Amp charger cut out after 4 hours 37 minutes when charging a completely exhausted battery instead of the expected 10+ hours!).
Alternatively, the seller said I could return the battery for a refund, but I could not send the faulty battery back to China
(presumably at my own expense) as it is illegal to ship faulty lithium batteries, and I was not prepared to risk being heavily fined for doing so.
I opened a dispute with AliExpress, and they eventually stepped in and agreed to my request for a 65% refund of the purchase price as compensation for the missing 65% capacity.
After receiving the 65% refund, I continued to use the battery for approximately 6 months before I eventually took it apart to investigate the cause of the low capacity.
I soon discovered that it was a 13S 4P pack made up of 52x 18650 cells. As real 5000mAh
(5A) 18650 cells did not exist, it was obviously never going to have had the stated 20 Ah capacity.
Whilst the pack was dismantled, I also noticed that the
BMS was only rated for 350 Watts and 15 Amps, which was very disappointing as the battery was advertised as being suitable for 1500W motors, and with a 30A continuous and 60A peak current output.
I decided to fit a more suitable
BMS (40A continuous and 60A peak) and after several charges I was able to fully charge the battery up to 54.54V, whereas the original
BMS was only charging the battery to 52.7V.
Since the replacement
BMS has been fitted, the highest capacity I have recorded on a single charge was 10.63Ah, and the battery gauge still showing 13% remaining, so it looks like the battery capacity might actually be ~ 12.8Ah, which is 82% more than its original 7Ah.
Unfortunately, if your battery is cutting out because of a very weak cell group, a new battery will be the quickest and easiest solution.
Alan 
