Stop Google Photos app from deleting a local album
One option is to individually open the photos and on the options menu choose "Save to Device". This creates a copy of the photo on your device and will be stored locally for a while longer.

Another would be to visit photos.google.com on a Chrome browser, and then select the photos and download to device.

The cached photos within the Google Photos app will not stick around for long. So it's better to have the relevant photos saved to device.