I have a Macbook and an iMac, and while both show Authorizing, only the Macbook actually seems to sync with Endnote on the web! I created dummy references on both Macs and only the Macbook reference shows on line.
Sorry to hear about your issues with EndNoteSync on your iMac. Just to confirm, after clicking “Tools>Sync” within EndNote on your iMac, do you see a Sync Status link on the Groups panel along the left of your library window? The mentioned Sync Status heading would appear below the All References group.
This may be due to the location of the library. Is the library stored on your local computer or a server location? We recommend keeping the local library on the local computer. Do you use any kind of cloud storage service, like Dropbox? Keeping a library in a cloud storage location can cause damage and lead to issues like this: