Your Nest thermostat in Las Vegas may be turning off for several reasons. The most likely culprit is power, specifically that your Nest isn't receiving the voltage it needs to keep running. In an HVAC system that uses a lower voltage than necessary, the Nest may give up trying to do its thermostat magic and, instead, just sit there and look pretty. HVAC systems that are older, are improperly wired, or simply aren't powerful enough to handle the job they're doing might cause this power issue. Ensuring that the common wire (C-Wire) is properly connected is step one for resolving this potential problem. If you can't it easily, get a hand from a professional.
Another likely reason is battery. If your Nest is low on power, it might be shutting down to conserve energy. This is particularly likely if your Nest has been installed in a space that's been prone to extreme temperature fluctuations. Lastly, if it's software-related, make sure your Nest is updated to the latest firmware.