Hi, hi again.
Problem with W3 Cache and may be some another plugins = present.
You plugin SET A COCKIES for 1 year. And if i CLEAN W3 CACHE, after i take a 400 error from nginx.
If i remove cockies (FROM YOUR PLUGIN ONLY!) - site work good again.
If i try to enter : /page/2 and if i try to clean W3 cache - BOOM! 400 error from nginx.
I try and check one cockie, and this cockie have a VERY LONG REQUEST.
May this help you to fix this bug.