I just checked the DA-40 POH (for the 1.7 Thielert-engined version). Indeed it's only got one (90A) alternator, but it's got no less than three batteries in the VFR edition:
- Main battery 12V, 35h Ah
- Alternator excitation battery 12V, 1.3 Ah
- ECU backup battery 12V, 12 Ah (powers ECU-B only)
The ECU backup battery should supply power to the ECU, if all else fails, for at least 30 minutes.
All true and you should get sufficient warning and have sufficient time to get the aircraft on the ground before the engine packs up.
However it is well worth having the backup battery under the back seat checked / replaced regularly. It should power the ECU for 30 minutes but, perhaps surprisingly, this assumes the battery is operating close to its maximium performance. In reality the batteries are often found to be way below their rated performance and 30 min is optomistic.
The sytem is OK but needs to be understood. I am not entirely sure you ever want to be worrying about the engine stopping on you while in IMC on partial panel and worrying whether you will get to your diversion quickly enough. Its fine for pottering around the local cabbage patch, maybe not really up to serious IFR touring.