I've been going crazy. I need to change my company email signature. I do so, it works fine but next time I quit Mail.app it goes away. I messed around with plists and permissions. Nothing helped.
Then I found an article HERE. It had the answer. I repeat it here for posterity.
The problem arises from some bug between Mail.app and iCloud Drive. The problem has been around at least since 2017. There does not appear to be a fix that will make Mail.app save signatures as long as it is involved with iCloud Drive. Fortunately, you can turn that on and off with no apparent harm.
Go to System Preferences->iCloud Drive, then click on iCloud Drives Options... button. In there, you will see a list that includes Mail. Uncheck Mail.
(Note: Mail appears in the list initially shown when you open the iCloud preference panel. This is not the correct one to uncheck. You need to click into iCloud Drive Options and uncheck Mail there.)
Back in Mail.app, you will find that signatures save correctly. Do your work. Quit Mail and reopen and you will find you new and changed signatures in place. Win!!
Once done, you can return to the iCloud Preference Panel->iCloud Drive->options and recheck Mail. Signatures will remain. Life will be good.