I was taught that you should never fly with a battery that couldn't start the engine on the ground, reason being that whilst jump starting the battery would get the engine going it would not solve the problem with the battery that left it so flat that it could not start the engine. It would therefore possibly not re-start the engine following an engine failure in flight.
That said, those for whom hand swinging is the only way of starting the engine will probably think the above argument is nonsense.
