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I don't think anyone has responded because there isn't a definitive answer to your non-specific question...
yes some betas (and iOS releases) have issues that may affect battery life. The way the OS chooses to manage tasks and programs affect battery life overall, but it doesn't affect your battery in a physical sense. and it certainly can't physically harm your battery.

Your battery's performance absolutely will degrade over time, there is nothing you can do to stop it, except taking normal battery precautions, such as not letting your battery run completely down and leaving it in a low charged state for any extended period of time. To a lesser degree, don't leave your phone on the charger for extended periods of time. li-ion batteries maintain their performance without degradation stored at about 80% charged.

If what you are really asking is how has the battery life performance been for users of ios6 beta 3, I can answer you that I have noticed improvements in battery life in IOS6, I charge my phone when I get to work at 8 in the morning, and usually on ios5 I was down to the low teens in terms of battery. On ios6, I am around 30-40%... I attribute it to the ability to turn on do not disturb mode during the night, so random alerts aren't pinging my phone throughout the night.
 
Still wondering if anyone knows if using the beta will decrease the performance and health of my battery quicker than a public release would

Thanks
Only because you may be playing with it, tinkering, exploring the new features more and running more battery cycles.
 
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