DriveHQ's FTP server supports standard FTP, SFTP and FTPS protocols. It works with all popular FTP client programs such as FileZilla, WinSCP, CureFTP, WsFTP, Fetch, etc. We have no other users reported any similar issues.
Based on your description, the problem seems to be caused by a bug in the other hosting site. You can verify it using any FTP client program such as FileZilla. You can upload many files/folders in one time. The other hosting company can also test it with FileZilla. It should be very easy for them to fix the bug since they were able to upload a few files successfully.
Please note that the FTP/SFTP service is a business feature. In general, users need to order an enterprise plan. The SFTP feature is only available to paid members, and is only available on proftp.drivehq.com. The free FTP service has a lot of restrictions, but it does not restrict you initially. Whether your free FTP is limited, you can find it out with FileZilla.