Okay, so when the engine dies, it won't start back up, e.g. starter motor will not turn. But, will start right up if a jump battery is connected?
If this is the case, then then either the battery is shot, or the engine is not charging it.
So easy to inspect / test the charging on this engine. Keep in mind, if it passes all the tests, you may have a bad battery or poor battery connections.
Inspect the regulator/rectifier; measure resistance using an ohmeter:
Next, check leads on charge coil; be sure to fully disconnect it, and it resistance between the leads to the coil should measure between
0.08~0.12 ohms.
Finally, carefully inspect the wiring harness, battery cables and terminals, etc. for any damage or corroded pins, plugs, connections.