If I understand you correctly, the external battery and probably the internal 740 battery were both dead or close to it. So the power drawn thru the 1 amp fuse was to charge the external battery, charge the internal battery, and power the 740. I'd bet that adds up to more than an amp. Ironically, I have the exact same setup and had the same thing happen today - I forgot to plug ships' power into the external battery, so the 740 drained the external and internal battery. It shut itself down as I was landing the first leg. After fueling the plane and ourselves, I plugged ships' power into the external battery, started up, and everything charged/worked fine. The difference is, I'm pretty sure I have a 5 amp fuse in that branch.