Hi Justinng0921w,
Thank you for posting in Apple Support Communities. We understand that when you attempt to do a screen recording while your iPhone is in Low Power mode, the recording will not save to your Photos app, is that correct? Does it save if Low Power mode is off?
If the screen recording didn't not save, unfortunately it is not possible to recover it.
Low Power mode should not affect your screen recordings from saving. To troubleshoot this, you can restart your iPhone and confirm that it is running the latest version of iOS 14 (14.6).
Restart your iPhone
Update your iPhone, iPad, or iPod touch
Hope that helps!