Ok, so now I've had the chance to examine the source code, and confirm the same thing happens if you're simply not connected to the internet, and also in mintUpdate 3.7.7 (Gloria)
The issue is on line 322 of mintUpdate.py where the condition always evaluates to false, since an empty file is written on line 310, hence the else clause is always executed, removing the backup copy of the rules file too.
Steps to reproduce:
1) ensure correct connection to internet
2) run mintUpdate, check the log has "++ Successfully downloaded new safety rules"... in it
3) verify the non-empty files /usr/lib/linuxmint/mintUpdate/tmp/rules and /usr/lib/linuxmint/mintUpdate/rules.old
4) disconnect the internet
5) run mintUpdate, check the log has "-- Failed to download new safety rules:"... in it, but not "-- Could not download safety rules"
6) verify the empty files above.
If you have a question that has been answered and solved, then please edit your original post and put a [SOLVED] at the end of your subject header
Hint - use a google search including the search term site:forums.linuxmint.com