Probably too late to help, but this will possibly help others who also experience this:
I had this issue while trying to quickly post thousands of messages (using requests.post in python). I found requests.post wasn't managing to post the messages quick enough to streamr. It was achieving very approximately 5 messages a second, but it wasn't fast enough and would cause unsent messages to build up.
I ended up using the grequests library in python (https://github.com/kennethreitz/grequests) which is much faster. In particular, the grequests.imap function.