There are now 3rd party sensor bars that offer both battery and Wii compatibility, if worst comes to worse. My cat chewed through my sensor bar's cord, and so I purchased a battery-powered one, and while it worked well, having to push a button to turn it on and off was a little annoying, and with lower power, the lights grew dim and difficult for the Wii-Remote to read.
Since then, I bought a new one, by "Gameshark," (I didn't know they existed anymore, but I believe it's now a MadCatz brand), that works with batteries or plugged into the Wii. For batteries, you have to turn it on and use a timer button, but plugged into the Wii, there's no difference between it and Nintendo's sensor bar, as best as I can tell. It was approximately $20, and unlike the first one I bought, it's no larger than Nintendo's bar. The first one was massive, FYI.
If I had to guess, I'd say the light bulbs in the sensor bar are beginning to burn out. That's my idea at this.