In situations involving lots of files, Globus Connect Personal can monopolize all the available data ports on the server, which can lead to a situation where all data ports are in use and new connections aren't allowed until the ports are freed, resulting in the message you report. Despite the faults being generated and the message, "ENDPOINT_TOO_BUSY" it is not necessarily an indication the transfer will fail.
One quick fix would you be to bundle (tar/gzip) the files before doing the transfer. Doing so before the transfer reduces the total number of data ports requested.