Yeah, my guess is the keyfob battery as well.
The wife called me from work when we were in Ottawa last winter, saying the car wouldn't start. She heard a clicking, but nothing more. This was in the 2011 Forester XT, which 100% doesn't have keyless start
The culprit was that she drove to work, parked, and turned off the engine; however, she left the key in the "on" position so that her seat warmer and bluetooth would work since she was on the phone with her mum. That conversation lasted 15 mins. The headlights (HID) were also on during the entire conversation despite the engine being off.
When she came back out to the car, it wouldn't start. A simple boost was sufficient, but the battery was weak to begin with (original, 6-years old - and the car only ever drives short distances). It ran "fine" for another few weeks until James Bergeron said, "dude, get a new battery". And so I did - went for AGM since it has a low self-discharge rate (anything helps...).