what Swoop asks about is my 'most likely cause' too, (best w.a.g., without a complete model and serial number, among other things)
but,,,
you should know that the manufacturer and OSHA all say the operators must be trained and know -not- to lift or lower while travelling, as it changes the center of gravity (more so with "a heavy pallet") in a manner that is 'less than as safe as possible", so actually watching the battery voltage AND travelling and lifting would not be the recommended manner to check the diagnosis, nor to operate the truck. I would suggest that you can stall the lift at full up for less than 3 seconds, and watch the battery voltage and get a much better idea and be 'more safe'. you will first want to read what the "at rest" voltage is, then compare it to the 'after 3 seconds hydraulic stall' voltage.

whats happening with battery voltage when this occurs?

sounds like the battery is dropping too low under power and is taking away power from hydraulics to run traction.