I finally replaced the battery and after installing the new one, the maintainer works fine. So in the end, the battery had failed during winter, while connected to the OEM battery maintainer. Al my cars are connected to maintainers during winter, but this is the first time it happens to me.
Unfortunately, I had to replace the failed Optima battery with another Optima unit, because the car's battery tray has the shape of the Optima, and a standard battery would not fit (I unsuccessfully tried with a Bosch).
I did the ECU reset process as described in the forum, but now I have another question: I assume that during its reset process, the ECU 're-learns' the octane level of the gasoline. It is well-known that the gasoline loses some of its octane rating during storage, and given that the gasoline has been sitting in the tank since I stored the car in December, it is fair to assume that the current octane rating is lower than that of 'fresh' gasoline. In this case, the ECU may not let the engine deliver its full potential.
Would it make sense to do another ECU reset process after topping-up next time, or should I assume that the ECU will constantly analyze the octane rating and will self adjust once I fill-up the tank again?
Current & past: 365 GT 2+2, 550 Maranello, F430 Scuderia
Other: Mercedes 230 SL 'Pagode', BMW M3 E30 Evo II, Lancia Delta Integrale Evo 2 and a few other toys.