Why would an airport have a beacon light on when there's no traffic? I live in a small town (Lone Pine, CA) with a tiny airport that sees a couple planes a week at best... busy-ish days when a major fire is happening. Over the past month the airport beacon light has been running all night long, never stops and I have seen one plane land. This never happened in the past. This just started. The lights shines in my window all night and I am trying to understand the reasoning behind it. 

I get airports need to have it on when planes are approaching but the question is why all night with no air traffic? Some say its broken and its supposed to be triggered by oncoming aircraft while other says its FAA regulation to have it on dawn till dusk.
The Chart Supplement says "Arpt bcn OTS indef."
("Airport Beacon is Out of Service, indefinitely")

It also says "ACTIVATE MIRL Rwy 16–34 and bcn—CTAF"
("Activate the Medium Intensity Runway Lights(MIRL) for Runway 16/34 and the Becaon, by using the CTAF")

Based on this, it is unclear if the beacon is out of service, or pilot-activated.
But it is clear that it should not be on all night.

A phone number is listed on that page for the airport manager, and I might start there.

After that, consider contacting the local Flight Standards District Office (FSDO).