Hi there.
Im experiencing similar issue. Hazel running on dropbox folder works well for some time until it stops processing the rules. Checking the rules preview the files are all matching still so the rules appear to be ok. Forcing hazel to run the rules on each folder works fine and continues to process the folder and files contained. Restart usually works to kick off the rules again as well.
Running OSX 10.10.5 Hazel 4.0.8 Dropbox 19.4.13
Multiple rules running on the dropbox folder stop processing at the same time
Heres a sample of one of the rules
If all is kind = folder
Run rules on folder contents
If all is kind is Archive
Move to folder _Temp_Unpack (local drive location)
Unarchive
Move to Unpack (box.com) folder