You can probably make a more educated guess than I as to why it malfunctions. My own guess is that some systems get into a positive feedback loop which may be induced by the tripod altering the resonant frequency to a point where the motion of the optics as they correct for shake induces a badly phased response in the motion sensors.
I did a little more digging last night and at least I found one place where Canon explicitly states whether a lens has a tripod compatible IS system and that's Canon's lens section
of their Camera Hall
. As an example, the entry
for the EF 300mm f/2.8L IS USM states "a tripod can be used with the camera shake correction function ON".
Of course, as a Sony man, this isn't of too much help to you but I can only speak to the system I know best.