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Life of an idle battery?

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"It depends". It depends on ambient temperature, whether you are using the app frequently to check on it, etc.

If the car is sleeping properly (i.e., you're not frequently waking it up using the app), and the ambient temperature stays above 50 or so, then you should expect to lose 2-4 miles of range per day (that's my experience).

I'd recommend calling around in the airport to see if there is a garage where you could plug it into a 120V outlet. Many places have them and are willing to let you plug in.
 
I left my car for about 10 days unplugged and lost about 2-3 miles a day. I checked the car every evening to monitor drain. The car was parked in an an open air parking structure and the ambient temperature averaged about 55 degrees fahrenheit.