Hi bigbear907,
Thanks for visiting Apple Support Communities.
It seems like your iPhone 6s turns off and has to be connected to power when it reaches 30%. Since the same thing happens after restoring from a backup, I would recommend restoring the device as new for testing purposes.
How to erase your iOS device and then set it up as a new device or restore it from backups
After setting up as new, you will need to enter your Visual Voicemail password for iPhone (on carriers that support Visual Voicemail). If you've forgotten your password, contact your carrier to help you reset it.
After erasing and setting up as a new device, your device is now in a factory configuration. Re-try what you were trying when you first found the issue to determine if erasing and setting up as a new device resolved the issue. Content on the device might have caused the unexpected behavior.
If the issue persists, you might want to contact Apple Support.
If restoring as new solves it, you may want to download content from the iTunes & App Store and/or sync your device again using iTunes/iCloud instead of restoring from your backup. You can use the following articles as a guide in this case:
Download your past purchases
iCloud - Learn how to set up iCloud on all your devices.
Sync your iPhone, iPad, or iPod touch with iTunes using USB
Sincerely.