I think if your time runs out it automatically resigns the game. It's just like when you run out of time in OTB. The rules are the same for correspondence games as far as I know. Hope this helps!
Error in "time-out" functionality

Yes, I understand that. But in this case, it´s a 1day tournament, and less than 24 hours have passed since I made my last move (thus also less than 24 hours since my opponent could have made his move), so how come I lose the match on time?

You have to make your move within the 24 hours. If you don't make it within that time period the game automatically resigns. Or are you asking if your vacation automatically activates for you if you don't make the move in time?
Hope this helps!

Ohhh,
No you don't lose if you made your move within the time frame like you said you did. If it's 24 hours and you make the move in 12 hours it will not time out. Hope this helps!

Yes again if you don't make the move on time it is treated the same as any other time control. Hope this helps!

Of course I understand that I lose if I don´t make a move. However, I did make a move, and 24 hours didn´t pass from my opponents move until I was timed out. Which is what I find really strange.

VladimirHerceg91, he's saying that he made his move in time, but lost anyway.
nes-q, did you perhaps forget to press the submit button? If you're absolutely sure that it is a problem with the site, you should submit an official ticket at https://support.chess.com/customer/portal/emails/new

Oh yeah, I once forgot to press the submit button. You have to move the chess figure and then press submit as well.
Yesterday evening I made moves in all my matches with less than 36 hours left before I was timed out. However, this morning, less than half a day later, I noticed I lost a bunch of matches in a 24 hours tournament. Have others experienced this?