This sounds like the update to the new project format; you should get a pop-up window telling you that it will be upgrading your project and creating a backup of the old version, which it does in place, next to the location where you had your project in the first place.
Do you get this behavior when opening the same project more than once? If so, are you opening the “backup” version, or the one with the original, non-“backup” name?
Right-click on the backup version (or try OPT, CTRL, or CMD while clicking); there should be an option in the pop-up window to archive it (.zip compressing it). After that, throw that copy into another folder (maybe create a Scriv v2.7 backups folder) just in case you need it some day.
You can find all of these project backups, in theory, by using the Finder to search for *Backup.scriv and then archive them all.