If you have a second person present who can operate the truck,while you take voltage reading of all the cells individually. Do readings of cells before you operate truck. The only function needed to operate is lift while you do voltage check on each cell. If you have access to a specific gravity reader you can check the state of cells. If a charger is not switching off ,then the charger is faulty. Check charger is correct for battery pack. you will need the large number on battery plate eg 500Ah this is battery capacity. divide it by charger Amp output. too high will cook cells

if you have a battery service company or forklift company you can contact i would suggest calling them out to check it.
They can do preliminary tests to determine if there is a deeper problem that would require repair or replacement.

My apologies the battery's are 37 volts and the charge voltage is 40 volts.
We put 32 liters of demineralised water in them.
The system goes through a normal cycle and shuts down.
i suspect the battery are faulty but I lack the facilities to load test them and check the volt drop across each cell.

if you have a 36v system the (charged) voltage should be reading approximately 37.5 to 39 volts depending on the condition of the battery.
If you are getting 27 volts then something is not right, bad cells most likely. You are checking the battery volts directly from the battery connector or posts?

have you tried load testing and checking batteries under a loaded condition?