Thanks Martin.
Yes, I have spotted the "save game" button now, too.
Weird, either I must have missed it (although I have been looking really hard), or it was added recently ?
Anyway, thanks, solved ... hopefully, unless they remove this functionality again. 
I think the game has to be at least 4 moves to save, so if it wasn't long enough, that could be it. I don't play bots a lot, but I don't think it's been removed since it was added.
@Martin: I think I may have found out what my mistake was:
The "save game" icon is on the game page, not the analysis page. Sometimes, I was looking for the button on the wrong page I think.
Another good thing was that bots allowed to play against a computer with a DGT board. Play / Computer does not support the DGT board, so now playing against the computer with the DGT board on chess.com is gone.
@danielbaechli:
what is the DGT board ?
@danielbaechli:
what is the DGT board ?
It's a board with sensors that can be used to transmit moves to a program. As discussed here, it would be transmitted to the live interface so you would make you move on the physical board and it will automatically be made on the site.
The software portion also works with other interfaces, so you could play against the engine in Chessbase, for example. Top tournaments also use them, where they transmit the moves automatically to a central location and can be viewed online, for example.
thanks, Martin!
Which button do you use?
If a game ends by resignation, I don't see any such button.
I see a Save Game option after resignation.