I do not think that is possible for live data connection. You might change it to extract and make custom schedules for extract refresh.
I do'nt want to use Extract Data, because i think connect live help me don't waste time and source system.
Another reason, when tableau server extract data, my system is much more low.
Okay, I think you are wanting to have different CACHE settings for each Site on your Tableau Server. That is not possible.