A few years later and I realize that this problem is more common that I thought.
After a full year of leaving my bike in the bedroom (annoying my wife, but I do not have a garage so...), resting around 40-60 percent charge at room temperature, as recommended for storage purposes in order to minimize deterioration of Li-ion battery, I can report the following.
I decided to take it for a ride without recharging the battery and it was horrible experience. Just maybe around a mile or so, taking it to a gas station to precisely inflate the tires and a circle around the block the motor was more OFF than ON. Ok, that is a bit overexaggerating, but I definitely experienced TONS of cut-offs.
My first step in attempt to remedy the problem was ONLY to remove the battery from the bike and recharge it fully. During the next ride cut-offs were SIGNIFICANTLY reduced. This gives me the impression that it is almost certain something related to internal battery wiring, whatever everyone else over the internet is saying (or at least it's part of the problem).
I tried to clean the contacts, both battery and Intuvia and they were already completely clean, so no change there.
And then I stumbled upon this excellent troubleshooting video by the Propel bikes (my issue with the Bosch is the first one described in the video):
I started my own diagnostics. Turned the bike on, waited for speed to appear on the screen to make sure everything is connected and then:
1) I unlocked the battery (Powerpack 500) from the bike frame and started to wiggle it around. Nothing happened. Then I started to pull it out of the contacts and it took significant length to pull before connection was lost and the speed disappeared from the screen. So I'm assuring you it has nothing to do with the battery-to-motor connection. That one is very sturdy and resilient.
2) I started to slide Intuvia display until it lost connection. This one took less effort, so I'm not excluding the idea that this is maybe the culprit. I also removed the screw which came with the bike, securing Intuvia display to the mount and making it unable to move. And I also loosen the bolts as recommend in the video but I'm not sure if it's just placebo. FYI, my Intuvia mount has all contacts in "gold color", if that info is relevant.
Anyway, now I get cut-offs rarely, almost exclusively related to hitting big bumps, BUT… Sometimes, when I turn on the bike, the display still doesn't show speed. At that moment, if I turn on the battery using the button built in on the battery itself, everything works fine.
Bottom line is that not a single solution you find online works 100% (including applying dielectric grease and updating firmware). If you ask me, there are ways to get around this but not to FIX it permanently. Bosch design definitely failed here and they don't want to admit.
I hope this will help someone
Cheers!