I'm in the same boat here - changed my battery from the original wet-cell battery to a Hankook MF42B19L sealed maintenance-free, and eco-idle decides to stop working on my 2013 Daihatsu Mira e: S. No idea what's gone wrong, and no mechanic seems to have a solution.
I read that a certain battery voltage needs to be reached before the eco-idle feature is turned on (presumably the battery is to be fully charged), and so I checked.
Standby voltage is 12.43v measured directly at the battery terminals with the ignition off.
With the car idling, it's 14.28v.
With car idling, air conditioning running, and headlights on full beam, it's 14.02v.
To my knowledge, these voltages are within spec, and don't indicate a problem with the battery or the alternator.
The regenerative braking seems to work just fine as well.
OBD2 registers no fault codes on Torque, and none on X431.
What I can't get a clear answer on is whether there's an auxiliary battery installed in the car, other than the SLI battery that I've had changed. Some people talk about the existence of some lithium-ion pack installed behind the backseat that I have found no reference of in the manual (which, admittedly, is in Japanese).
At least that would give me one more thing to diagnose.
Right now, I have no idea what the hell is going on.
@xulfiqar, any thoughts?