Hello Dr Green
The Honda engine does indeed trickle charge whist its running, albeit at quite a low rate. If the machine is being used for lots of short periods the charging may be insufficient to replace the power lost from the battery during the cranking/start operation.
Would be worthwhile getting the battery checked in the first instance to make sure its holding the charge OK.
The charging system is integral within the honda engine but the rectifier is connected outside of the machine via a green plastic multiplug, check both parts of the multiplug are pushed fully home and all the wires within it are connected and without corrosion.
If the battery checks out OK I would take the machine back to the company that fitted the engine to check it out
Timberwolf have a Technical helpline on 01449 765820 if further advise is needed