I carefully tag all my photos but the next time I start the program my tags don't always show up. Once I correct the missing info and backup Pse and then restore it, all my corrections disappear. Frustrating. Why isn't there a "save" feature so the corrections I made will still be there when I start the program again?
What OS and version of Elements are you using? I know very little about Macs, but I have never heard of anything happening like what you describe on Windows. So, before we figure out what you are actually doing (and why), I can tell you that any keyword tags that you apply to a file in the Organizer can be saved to the file by using the File>Save Metadata to File command (or use Ctrl/Cmd+W).
So we can understand your problem a little better, please explain the following:
What kind of tags are you applying (keyword tags, People, Places, Event tags)?
How are you applying the tags?
Where do you think the tags are not showing up?
Are you in the Details view or the default amorphic view? (Press Ctrl+T to toggle the Details view on and off)
How are you backing up and restoring the catalog? Are you using Elements or some other software to do so?
If using Elements to backup and restore your catalog, what options are you using for the restore? How many backups do you have?
An answer to all my questions may help us figure out why you are experiencing the problems you describe.
Added: And here is another question that may be important. Are the tags not showing up in images at the top of a stack or a version set?