Interestingly, 16381 is so close to power 2.
This is basically an assumption:
I am wondering this is an OS thing. Looking at the TPS data, is a new connection created for each transaction? [Edit yes, now that I have read your question correctly.]
Perhaps the OS has only so many connection resources that it can use and cannot immediately create a new connection after it made 16381 in the recent past (plus a few extra ones)?
An OS parameter can be set to indicate the number of available connection resources, which allows you to use more connections. Can you add some OS details to the question?
In particular, I suspect that the port number with which you are connecting is constantly increasing, and you click the limit. Try "lsof -i" and see if you can catch the connection somehow, and see if the number grows.
Edmund
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