Thanks @Boki_Srb and @Midnight Blues for your suggestions.

I have just done a test: with the battery fully charged the device ran for 75 minutes in daytime with the screen at maximum brightness, then the low battery warning came up. I guess that means I can eliminate the battery as the problem.

That just leaves firmware or the device itself. I will borrow my friend's identical unit and see if I can find a way to copy his operating system. I'm not even certain this is possible, lots of nonsense about WinCE on the internet when I google for it

This will have to be after my holiday as I don't want to brick my device and have to find my way through the Pyrenees with paper maps!