As a data point for future googlers, I had what sounds like the same/similar problem today, my middle-button-click stopped working.  

Except I found that it was working but I had to hold it down for a few hundred ms until it reliably clicked, sometimes quickly clicking in succession would report some clicks also, but holding it down for about half a second was reliable (but annoying).

Anyway, long story short I issued the following set-prop for "Evdev Middle Button Timeout (269)" and it corrected the issue, note that I also first tried changing the property to 10 first and that didn't make a difference, but now after having set it to zero I can increase that property to seemingly anything and it all works fine, so I don't know what exactly is going on there.

xinput --set-prop 11 269 0

(where 11 is the device id of my mouse (xinput without arguments will tell you), 269 is the property being set, and 0 is the value I am setting, 

Here are the list-props when I was experiencing the problem

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Device 'MOSART Semi. 2.4G Keyboard Mouse':
        Device Enabled (131):   1
        Coordinate Transformation Matrix (133): 1.000000, 0.000000, 0.000000, 0.000000, 1.000000, 0.000000, 0.000000, 0.000000, 1.000000
        Device Accel Profile (258):     0
        Device Accel Constant Deceleration (259):       1.000000
        Device Accel Adaptive Deceleration (260):       1.000000
        Device Accel Velocity Scaling (261):    10.000000
        Device Product ID (248):        1578, 16641
        Device Node (249):      "/dev/input/event5"
        Evdev Axis Inversion (262):     0, 0
        Evdev Axes Swap (264):  0
        Axis Labels (265):      "Rel X" (141), "Rel Y" (142), "Rel Horiz Wheel" (255), "Rel Dial" (256), "Rel Vert Wheel" (257)
        Button Labels (266):    "Button Left" (134), "Button Middle" (135), "Button Right" (136), "Button Wheel Up" (137), "Button Wheel Down" (138), "Button Horiz Wheel Left" (139), "Button Horiz Wheel Right" (140), "Button Side" (253), "Button Extra" (254), "Button Unknown" (251), "Button Unknown" (251), "Button Unknown" (251), "Button Unknown" (251)
        Evdev Scrolling Distance (267): 1, 1, 1
        Evdev Middle Button Emulation (268):    0
        Evdev Middle Button Timeout (269):      50
        Evdev Third Button Emulation (270):     0
        Evdev Third Button Emulation Timeout (271):     1000
        Evdev Third Button Emulation Button (272):      3
        Evdev Third Button Emulation Threshold (273):   20
        Evdev Wheel Emulation (274):    0
        Evdev Wheel Emulation Axes (275):       0, 0, 4, 5
        Evdev Wheel Emulation Inertia (276):    10
        Evdev Wheel Emulation Timeout (277):    200
        Evdev Wheel Emulation Button (278):     4
        Evdev Drag Lock Buttons (279):  0


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Here are the list-props after issuing the set-prop command above

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Device 'MOSART Semi. 2.4G Keyboard Mouse':
        Device Enabled (131):   1
        Coordinate Transformation Matrix (133): 1.000000, 0.000000, 0.000000, 0.000000, 1.000000, 0.000000, 0.000000, 0.000000, 1.000000
        Device Accel Profile (258):     0
        Device Accel Constant Deceleration (259):       1.000000
        Device Accel Adaptive Deceleration (260):       1.000000
        Device Accel Velocity Scaling (261):    10.000000
        Device Product ID (248):        1578, 16641
        Device Node (249):      "/dev/input/event5"
        Evdev Axis Inversion (262):     0, 0
        Evdev Axes Swap (264):  0
        Axis Labels (265):      "Rel X" (141), "Rel Y" (142), "Rel Horiz Wheel" (255), "Rel Dial" (256), "Rel Vert Wheel" (257)
        Button Labels (266):    "Button Left" (134), "Button Middle" (135), "Button Right" (136), "Button Wheel Up" (137), "Button Wheel Down" (138), "Button Horiz Wheel Left" (139), "Button Horiz Wheel Right" (140), "Button Side" (253), "Button Extra" (254), "Button Unknown" (251), "Button Unknown" (251), "Button Unknown" (251), "Button Unknown" (251)
        Evdev Scrolling Distance (267): 1, 1, 1
        Evdev Middle Button Emulation (268):    0
        Evdev Middle Button Timeout (269):      0
        Evdev Third Button Emulation (270):     0
        Evdev Third Button Emulation Timeout (271):     1000
        Evdev Third Button Emulation Button (272):      3
        Evdev Third Button Emulation Threshold (273):   20
        Evdev Wheel Emulation (274):    0
        Evdev Wheel Emulation Axes (275):       0, 0, 4, 5
        Evdev Wheel Emulation Inertia (276):    10
        Evdev Wheel Emulation Timeout (277):    200
        Evdev Wheel Emulation Button (278):     4
        Evdev Drag Lock Buttons (279):  0

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