I've read that this happens when there is a function like NOW(),
TODAY(), etc...

However, I am still getting the save changes prompt on a variety of
workbooks despite not having any of these functions. What they do all
have in common though, is they use the SUMIF function quite liberally.
Would this be a cause of this phenomenon, and if not, is there an easy
fix?

Here's an example of a SUMIF function that I believe might be causing
it:

=SUMIF($B$10:$B$370,"SMG Total",J$10:J$370)+SUMIF($B$10:$B$370,"BHT
Total",J$10:J$368)+SUMIF($B$10:$B$370,"GJC
Total",J$10:J$368)+SUMIF($B$10:$B$370,"KAM
Total",J$10:J$368)+SUMIF($B$10:$B$370,"JLY
Total",J$10:J$368)+SUMIF($B$10:$B$370,"MAJ
Total",J$10:J$368)+SUMIF($B$10:$B$370,"RLP
Total",J$10:J$368)+SUMIF($B$10:$B$370,"CCM
Total",J$10:J368)+SUMIF($B$10:$B$370,"KRA
Total",J$10:J$368)+SUMIF($B$10:$B$370,"MEH
Total",J$10:J$368)+SUMIF($B$10:$B$370,"GPA Total",J$10:J$368)+J160