That's interesting that it failed that badly on an 11mm. I often felt that the use of a 10.5mm rope was slightly pushing it, it had that same not quite right feeling like using a Stop on an 8mm rope, but I would have thought it solid at 11mm.
With weighting the rope, my recommendation was to add a kilo or so at the bottom, which would be likely smaller than the weight of the rope on a climb. I can see the reason for concern though. (Obviously it was also backed up by a different device, either a shunt or a basic on a separate line.)
Though it was a couple of years ago, I believe I recall the Rocker locking more consistently onto rope loaded with a few kilos. I think when there was little weight on the rope the rope could come into the device almost horizontally and feed through quite happily in a gentle curve without troubling the device (though not without troubling the user!). A bit like depicted in
http://blog.climbtools.eu/index.php?rex_img_type=leftright&rex_img_file=12_rocker_belastet.jpg
but with greater radii of curvature of the rope. Perhaps the stiffness of the rope could be a variable.
If there was a lot of loading on the rope, such as someone standing on the end, it would lock but then the elasticity of the rope would 'bounce' the device back to unlocked and you'd drop another couple of metres before the process repeated.
As for abseiling with a Rocker or Shunt on the rope (on a cowstail and above the abseil device), I never had any problem (on used 10.5mm) rope getting either to lock. An ab that was too rapid would simply cause the Rocker to move up the rope faster than it slipped down, load the cowstail and lock. With the shunt, letting go of the tow cord always caused an immediate stop.
Its quite possible that these observations mislead me as they weren't rigorously scientific. It's interesting and concerning though that people can have very different experiences of the same piece of kit.