Thank you for your message. I am sorry you are having this problem.
Favourites are stored in the browser cache. Are you looking in the same browser on the same computer they were favourited?
Unfortunately, if you are using the same browser on the same computer and they are no longer there, they are most likely gone forever.
If anything deletes things in the cache or all of the cache, your favourites will disappear. Some examples include:
Is your disk close to full or do you have a limit set in the browser of how large the cache can be? If so, the browser might be deleting things in the cache to conserve disk space, which would delete your favourites.
Do you have a utility program that is being run manually or automatically to clean up your computer? These utilities frequently delete browser caches to recover the disk space. That would delete the favourites.
Do you have a browser extension which is deleting things from the cache? Try using another browser for a few days and see if you experience the problem (but note that any images you favourite in that browser will only be available in that browser.
I said "most" likely gone forever, because there are steps you can take to rewind your cache if you had already been backing it up, but most people do not do that. My primary platform is Mac and I back my browser cache up with Time Machine on the Mac, so I can go backwards in time and restore my cache from a point in time. This has saved me a few times when something was deleted from my cache and I was able to roll the cache and settings back a day. If Windows was my primary platform, I could do something similar on it.
For a complete description of existing features to save prompts and images, please see these documents: