You mentioned that this happens when the mic is turned off. I doubt that your problem is related to the battery. If the transmitter (mic) is turned off, the receiver can still "look" for a signal and generates a noise that sounds like static or hiss from a 500 pound snake.The best way to prevent such events is to mute any channel not being used. Closely monitor the activities of the folks on the stage. Most people have to look for the off button on the wireless mic, in order to turn it off. I suggest you beat them to it. Mute the channel.
If your board has no mute button you can either shut down the channel fader, or input gain trim knob. A word of caution here. On some boards, depending on how you are running the channel strip, killing the output fader may still have the hiss show up in the monitors. In that case mark the level where you run your input gain, and use the input gain knob to mute the channel at the incomming signal point. If your board has a mute button, use it. This is better than having to re-set the input trim. It's quicker too.
I agree with the comments on the batteries. Once the voltage drops, a diversity system will seek the stronger signal. A non-diversity signal will drop out. The lower the voltage goes, the more drop-outs will occur. My advice is to replace the battery before each service, or invest in a quality battery voltage tester. They are inexpensive, and give you a good idea of the risk associated with using a particular battery again. The good news is, there won't be any drop-outs in heaven.
Hope this helps you.