The system will turn off if the pressure is to high or is to low. Generally when it's too low it will cycle on and off though so you may have something else going on too. I've never done work on the Viper AC system but have worked on dozen's of other cars. You generally have pressure switches that will tell the computer if things are to high or low. If they are triggered the system shuts off to protect itself. It's possible its one of those. Sounds like you've found the sensor though already. It's possible it's bad as well.
The heat aspect is what makes me think charging issue. Freon pressure goes up with heat so if it was borderline at the start it will be to high and thing will shut down. But when you say you ran it with only 10oz in the system and it still did that, that starts to make me think I'm wrong as it wouldn't do that at that low of a charge. Worst case it should cycle.
Looking at the schematics, maybe check on the AC thermostat. Item 10 here. I'm not familiar with them so can't advise on how they interact with the system but if it makes adjustments based off temp readings it could be faulty and causing things to shut down.
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