Programmable light switch failing or acting oddly?
Your switch is wired up wrong
The RPLS530 does not require neutral, according to its instructions; however, yours appears to be incorrectly wired.  According to the instructions, C and 2 need to be connected to the incoming hot in a single-pole setup like yours, while 1 connects to the switched-hot off to the fixture.  I would expect the switch to function incorrectly in your current wiring (with 1 and 2 to always-hot and C to switched-hot); however, it does not explain your current behavior, so I would suspect the switch has failed, based on the troubleshooting you've done so far.
It appears that you have no neutral at the box
Furthermore, it appears that you have no neutral at your switch box, since I see no wires spliced through in the back of the box in your picture.  This means that you'll want to go with another RPLS530A, or a similar type that does not require neutral, as your replacement switch.  You'll need to obey the device's minimum load rating when you do, though; for the RPLS530A, you need to provide at least 40W of load for the switch to power up properly.