Should I uncheck the box in my backup software that says "Replicate Folder and File Deletions?"?
Your backup software should never be deleting content from the backup. It should merely remove the file reference from the latest incremental snapshot, and you need to keep enough snapshots to take you back several weeks or even months.
Personally, I take a backup set out of rotation every 3 months or so. I ought to be able to restore
anything from the last 2 years. Whether I can find it (or even remember I had it) is another question entirely.