Reappearing files and folders usually occur because one or more of the computers that are synced are still accessing the folders.
You should delete the files from the Dropbox folder on the computer that's recreating the file. You can see which computer has re-added the file by going to the website and checking previous versions of the file.
Please see here the instructions for checking a file's version history.
Have a lovely day!
Re: HELP: Dropbox automatically re-adding my deleted files!
They're JPEGs (~2000 of them) used by Tap Forms (synched database). The only way I could stop it (I think, but it's been a few hours now, so I'm hopeful) was to delete the files using Finder on both iMacs and then log out of the user account and then delete the Tap Forms app on iOS. Then, using a different user account log on to Dropbox via the web and delete everything there too.
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