I'm a bit confused here. Are you saying that the shifter physically changes position and goes to Neutral? = Check shift linkage.
Or are you saying that the transmission is slipping while driving in gear? = Burnt clutches, bad pump, or bad converter. Rebuild/replace the entire setup.
Is this a th350C with a lockup converter? If not, turning the car off won't reset anything and the only way it would help is if things were too hot, in which case you'd have to wait a while for a change to occur. The th350 has a mechanical speedo, vacuum modulator, and a cable to drop a gear when passing: i.e. no electronics. The "C" model has a lockup style converter which I won't even begin discussing, but there's a solenoid that can become stuck and turning the power on/off can occasionally help. They're not incredibly common.
I hate to ask, but are you 100% sure on the transmission model the car has? An old friend of mine had this exact issue on a 2004R, which is an entirely different system. We'd sometimes have to kill the ignition while rolling down the highway.