Yes. Even with 1 GB of ram, my game still quit after playing it for quite a while (say 30 minutes).With 1GB of RAM, you don't even have half that for your apps and games. The most I ever saw free on my iPad 2 Mini was 350mb if I manually went in and closed every app that was running...
I don't think 2GB of ram could improve it a lot, though I may encounter less safari tab reloading (which is annoying). And in this iOS 9 beta 1, unlike previous version, you may only realise it is reloading when you see progress line filling up the bottom line of address bar, while page content will display on the screen, letting you think this tab was not reloaded. This becomes even more annoying.
However, since Apple always push hardware just behind the software requirements bar, I doubt even 4GB of ram could bring us better performance than what we are using with only 1GB or 2GB of ram.