The customer's issue seems to be that they have a very large number of files, and are trying to sync it with a 32-bit desktop client, and are hitting memory issues.
Dropbox themselves state this on their websites:
https://www.dropbox.com/help/space/file-storage-limit
> Note: The performance of the Dropbox application may start to decline when you store above 300,000 files.
I've done some comparisons across various companies sync clients, and it is a tricky problem.
(Disclaimer: I work for Google).