This is not an answer, like a push in the right direction, but start here:
:help quoteplus :help x11-cut-buffer
In particular, in the text of the second help there are some interesting notes on the suspension of vim. It claims to write a buffer in PRIMARY and CUT_BUFFER0, so you can use the middle click after you pause it. Maybe you removed those or a plugin that interferes? Perhaps you are using an old version of vim (I am running 7.2.182).
My suggestion is to disable all plugins that you installed manually and try vanilla vim. If this does not work, consider using vim -V (verbose) and see if it tries to put a buffer in PRIMARY or CUT_BUFFER0 before it is blocked.
I don't have vim compiled with X (vimx), so I can't verify this myself. Hope this helps you in the right direction.
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