The battery is bang on. I've used the car all week so there will be plenty of charge in it. I sometimes don't use it for a month or so (esp in winter) and it always starts first time, no semblance of weekness.
Because of the intermittent soldering issue (with the power coil most likely). Some mechanical stress on the parts while the batteries were replaced brought the solder connection back, for a while.
Owners often report that the key works if they put it into the EIS and simultaneously operate remote control. A similar case.