If you leave a ball both your stamina and confidence go up by 1% to 3%. I use this approach in Tests and Odis to manage stamina.
Do you have to actually 'leave' to get that or can you just not play a shot? I got a bit paranoid about pressing the actual button to leave after seeing some of the edges people were getting from it in the last game, haha! Shame if blocking or even just not running doesn't help too though in some way - hard to comment much without first hand experience though.
Does it make a difference if you can rest at the non-striker's end, and can you see a difference between players with high and low cardio fitness ratings? Would be nice to see the system being well-balanced anyway. It would actually mean you'd be trying to hang on to the close of play sometimes, knowing your stamina would be boosted if you could keep your wicket until the morning and things like that.