Press "P", that's it.
I have had this issue too where my keyboard all of a sudden doesn't control time anymore. It has happened across households.
I also have a lsighty related problem where I click and/or press ~ to pause the game (or any other time control) and nothing happens. I still hear the sound in game that I've pressed pause, but the game does not actually pause. My Sims move around like nothing happened. Then, usually a few sim hours later, the game will "catch up" with the pause button and will pause. I've also noticed that when it does eventually pause, the time will revert back to whatever time it was when I pressed the pause button. I've also tried to open the menu in game, thinking that it would pause the game for me, but I can still see my Sims in the background moving around like normal.
