I also drive a 2006 Altima S, Special Edition and have had the exact same issues. I have already been using the aux mode (turning the key half way) to pressurize the tank and that seems to have solved it for now but I would still like to fix the problem.
Did you ever hear anything from the dealer when you took it in? I am out of warranty and have about 92000 miles on the car.
My car doesn't always have the issue when its hot or cold in particular but I think its more frequent when hot. When it does hesitate, it only struggles and will eventually start but it seems really rough and can't be good for the motor. My battery checks out ok. I just replaced spark plugs. Starter sounds fine. I've also experienced the partial filled tank but I've never had a problem and it's done that for 4 years.
Thanks