If you have 8 GB RAM, that's probably not the issue, unless you have a bunch of browser windows open at the same time or you never restart your computer. The limiting factor will be Cider, which is unavoidable on macs and can never use more than 2 GB for TS3 at a time. And you're right that a long-running save will need more resources to play than a new one.
To give you an example, I have only the base game and Ambitions installed on my macbook (as well as some SPs, which don't really add to overhead). When I start a brand new game in SV while offline, the RAM load is about 1.50 GB initially and rises very slowly, meaning I can play for hours, especially with a single sim. When I start up my most recent game, which I've been playing for 4 sim weeks with a family that's grown to 14 sims, the RAM load is 1.71ish on startup and gets to 1.9 in just over an hour. At this point it's time to quit to desktop and reload.
As many simmers can tell you, the EPs Seasons and Pets, followed by IP and ITF, are particularly resource-heavy and will push you over your RAM limit pretty much no matter what you do. Snow is especially demanding, as are various issues related to stray animals. The real tech experts will tell you that even trying to run these EPs on a mac is probably a lost cause. I'm actually about to Bootcamp my new computer (with Windows 10, unfortunately, although you might have to use an earlier OS), as this is the only practical way for me to add more packs and still play TS3 the way I want to. If this is something you're interested in, igazor plays on a Bootcamped imac that's about as old as yours and is pretty happy with the experience. Tag him if you'd like to ask about it.
I'm sorry that you can't play TS3 on your mac the way you want. It's so frustrating when something that used to work just starts acting up with little explanation. I hope you can find a way to still enjoy the game, but with a 2 GB hard limit on a mac, you're never going to have a lot of room to maneuver.
Edit to add: TS3 has some issues with RAM leakage, as in, it doesn't always release all of the RAM it's no longer using. You can address this by
purging RAM periodically using Terminal. I've found that this only helps a little bit, maybe enough to compensate for the memory spike when I try to save but not much more than that. If I launch the game with wifi on (even if I don't sign in), the command will purge something like 20-30 MB right away—probably the leftover stuff from EA's in-game shopping experience that gets loaded even if you have it turned off. (Check your FeaturedItems folder in Documents for the unwanted content, and you can delete anything you find there.) But if I'm not online, purging will only free about 10 MB for every sim-day played. Still, it might be helpful around the edges.