I took your advice and tried playing the file with VDPAU in SMPlayer. Worked perfectly even with the desktop effects enabled. No visible dropouts.
The file also played perfectly in Xine, after I set Audio to ALSA. Auto and PulseAudio gave me no sound at all, but PulseAudio has given me trouble before. That Xine worked so well surprised me as Kaffeine failed so miserably, but of course Kaffeine uses its own config file for Xine, and as you can't edit it from the GUI I didn't try editing it at all.
Loopy, on the other hand, only played the sound now. The upgrade to KDE 4.6.1 seems to have broken it.