I am sad to report that this problem came back with the FP6.QREL.16.69.0 update.
The problem was gone for some time after I did one of the thigs that @yvmuell suggested (see my post from Apr 17).
However, like the previous time, when I updated to the latest software, the problem came back. The phone now uses again 10-15% in a couple of hours in airplane mode. And again, I am not able to go 2 days without charging, but only one.
I tried the same procedure, but it is not working.
I downloaded AccuBattery and I saw that most of the days I get 0h 0m of deep sleep, sometimes I get around 1h for the whole night that the phone is on airplane mode not being used.
I also installed BetterBatteryStats Reloaded, but I have no idea on how to work this app to figure out what is keeping the phone from going into deep sleep. Does anybody know what I should look for? I think that with BBS I will be able to find it pretty easily.