That setting under Advanced Tools only sets a cookie so it only affects you, you would have to disable it from web.config to disable it for everyone, otherwise others might be getting an error or no css even though it works for you.
I would enable caching and check it with firebug to see what is going wrong, is the css url returning css or getting an error or something.
That error about out of memory can happen in cheap hosting if they don't give you enough memory and it can lead to poor performance if it causes the app to recycle frequently which typically happens whenever the memory limit is reached. Also if you have any custom features you need to be careful in developing them that they don't consume too much memory or have coding errors that cause a memory leak. However unless that error is happening right at the time when the css is not working it is probably not related.
Hope it helps,