A Pilot spends most, if not all of his time at the controls. So you should too....

I did a seven hour flight today, and I was near the computer almost the entire time. I usually don't do long flights like that, but I had a lot of homework, studying, and reading to do today. I did have to take several long breaks, but the sim was paused. I do all my flying, at real time, and at or near the comuter. I have done several flights that lasted over 10 hours, and even over 15 hours. Sometimes they would take a couple days, and I would have to save the flight, and continue when I had more time another day.
But anyway, when ATC hands you over to another frequency, acknowledge, but don't contact the next controller. You won't be penalized, and when you're ready to continue ATC communications, simply contact the controller and follow usual communications.