I am currently in my second photobucket account, I've used up the first account.
This is the first photo I think I saved...

It is also one of my very first photoshops.
I think if you move photos from folder to folder, you lose the links to the photo. I also think photobucket has some kind of image filter that deletes questionable photos for content....it may also filter by file name.
1. Create folders in you photobucket account
2. Download your photos into specific folds so you won't need to move them later.
3. It may help to copy and post the direct link vs the html links to the photos (I don't know why that would be an issue, but I only copy direct links)