Without examining the actual Finale document we can only guess.

There are several possible culprits.

1) Make sure that all the whole measure rests are Default Whole Rests (so that the measures are truly empty), not Real Whole Rests.

You can use the plug-in:

Plug-Ins menu > Note, Beam, and Rest Editing > Change to Default Whole Rests

2) Make sure that there are not any staff styles that prevent the multimeasure rests.

Finale does not consider a measure truly empty if the measure contains a staff style with e. g. Blank Notation, or Slash Notation, or One-Bar Repeat, or Two-bar Repeat.

3) Make sure that there are not any expressions that are defined to “Break Multimeasure Rests”.

4) Make sure that there are not any measures with, in the Measure Attributes, selected “Break a Multimeasure Rests”.

Still no luck! The other day, I got the multimeasure rests ok - the next morning they had disappeared! I went through what you suggested, it didn't help!

… The other day, I got the multimeasure rests ok - the next morning they had disappeared …

Is the issue document specific (= only in some documents) - or is the issue program specific (= happens with this copy of Finale, in all documents)?

Have you tried “the usual steps”?

I mean

- close the document, and open it again,

- quit Finale, and launch it again,

- reboot the computer,

- (as a test, not a solution) try it in a brand new user account,

- quit Finale, remove its Preferences file, and launch it again

Not to mention going to the full score and using the Edit > Multimeasure Rests option to create them for Score and Parts (if nothing else has worked).