NASA Moves Longest-Serving Mars Spacecraft for New Observations from February 2014 mentions Odyssey's battery:
Odyssey flies in an orbit nearly over the poles and synchronized with the sun. For most of its first six years at Mars, the orbit was set at about 5 o'clock, local solar time. At every spot Odyssey flew over as it made its dozen daily passes from the north pole region to the south pole region, the local solar time was about 5 p.m. Beneath the south-to-north leg of the orbit, the time was about 5 a.m. That orbit provided an advantage for the orbiter's Gamma Ray Spectrometer to have its cooling equipment pointed away from the sun.
Later, Odyssey worked for three years in a 4 o'clock orbit. [...] This timing, however, added stress to Odyssey's power system. It put more of each orbit into the planet's shadow, where solar panels are unproductive. After providing radio-relay support for the 2012 landing of NASA's Curiosity Mars rover, a maneuver set Odyssey on a slow drift to later times of day to help preserve the spacecraft's aging battery.
This indicates that the battery was at least healthy enough to be a part of normal operations (used every orbit during eclipse) until late 2012. The 4 o'clock orbit (and 16 hrs antipode) has parts in Mars' shadow whereas the 5 o'clock (and 17 hrs antipode) does not as shown by this diagram I made of Mars solar time (400 km orbit height according to Wikipedia):