After my question I lowered the reconnection period to 30 minutes for tests and it then seemed to work (that said I witnessed up to 1h since last login despite the 30m period but at least it connected to fota web more often than before). I think I had disabled deep sleep when testing with the 30 minutes period. I've then set the sleep setting back to deep sleep and the fota web period to 2 hours, since then the device hasn't connected for the past 20 hours despite vehicle movement, ignition, sent SMSes, ...
Not sure if the sleep setting and/or longer period are the culprits. Maybe I don't understand how the device is supposed to connect to fota web, or there's a bug in the firmware, or there's a problem with the service itself (see this question).
[edit: I just realized you were the OP of the question I've linked to]