Just wondering if anyone has had the same problem I have, and what I could be doing wrong. I've played a lot of hours but don't claim to be an expert.

I've had several times where the time appears to be stopped (the "time stopped" text appears on the screen and the icon is checked off in the options screen) but when I check back days later, time has continued and most of my fish are dead/nearly dead.

OK, I didn't check the forum today before I posted. Then I see there is the same question!
Mistake noted - sorry everyone.

That sounds like something that happens as a result of how the game handles multiple player slots and tank updates. If you're playing games in more than one player slot, there are some precautions to observe once you return to the game. Due to the way that the game updates the state of your tanks, you should always click Play immediately after changing players. If you don't do that, you can experience unexpected results. After you've clicked Play, it's safe to return to the menu and change the game speed.

If you go to the menu and change players, then change the game speed before you click Play, the game will ignore that you had it paused all that time and update all of the fish in your tanks at the new speed setting when you click Play. Basically, the game doesn't know you had Stop Time set if you change it to something else before you click Play (and your fish will be in the same condition they would have been if you'd left it at that speed setting when you last saved the game). You must click Play immediately after switching players if you want to preserve your game speed setting (whether that's Stop Time or any other game speed setting). Once you've clicked Play, you can go back to the menu and change the game speed.