Did you check in Settings > Battery to see what might be draining the battery? If it's something like rapid battery self-discharge (which is unlikely but I've seen it occasionally) it wouldn't show up there as anything using up the battery.
About the battery usage on your iPhone, iPad, and iPod touch - Apple Support
I personally leave my devices connected to power overnight. There's nothing about doing so that would damage a battery. And it might be better than accumulating charge-discharge cycles that could be avoided by simply making sure it's connected to power to handle its active power needs.