The following may not be relevant to you, so please ignore it if it's not.
Firstly Grappling when you are tired and your strength is low is a good thing. It forces you to use technique and gets you used to that "I can't go on" feeling. It sounds like you are really reliant on strength and grappling when tired will force you out of that.
You can't really expect to go full out for that period. Another thing is that you say your "hell on wheels" for the first 20 minutes. Maybe you should relax a bit. It is less work and more effective to turn on the power/strength suddenly rather than grapple all the time at 100% time.
I'm very aggressive and it took me some time to apply above!