@Wasd 

I still cannot understand what is going on when this happens. Sometimes everything is ok for days, then it gets screwed every day. The most interesting thing is that the problem just gets solved by itself in the night, at around 1 to 3 a.m. It is like an inverse Dr. Jekyll and Mr. Hyde. Anyway, I have no problem since a few days now but no update happened, so I still cannot believe that this pain flew away...

I guess you don't use cable connections but if you would they wouldn't show up either on the start page. 

@Wasd 

Well, let's hope the best. I've been using using this range of IPs since the beginnings and I still experience this crash sometimes.

@Simion 

Yes, reboot was the first thing I tried. Sometimes it helped, sometimes not. Since a few weeks I don't experience the bug but I did for 3 months, since I bought the router.

Now I don't check it so often and when I do, it seems ok. But because no firmware update were installed and the reboot did not help every time, I still cannot believe that it "healed" itself permanently. As the problem comes quite randomly, it can stop randomly, too. I'm using my router/modem in cellular modem mode. It has also happened once that the data usage counter had not been reseted on the day, which I set as the end of my billing cycle. This was the main reason I logged in every day and checked my data usage, not to get an overusage fee.

UPDATE:

Yesterday I checked it and it was crashed again. I did not make a reboot because in this case I should have done it for a few other devices at home, as well. The problem presists today but I don't care. It may fix itself sometime.