Switching the X11 acceleration method from sna (default) to uxa by adding
Option "AccelMethod" "uxa"
to the Device section of /etc/X11/xorg.conf seems to have solved the problem, although (a) it's a bit hard to tell as the problem was/is intermittent, and (b) there is probably some performance cost to the switch (although it's not noticeable to me).
Switching the X11 acceleration method from sna (default) to uxa by adding
Option "AccelMethod" "uxa"
to the Device section of /etc/X11/xorg.conf seems to have solved the problem, although (a) it's a bit hard to tell as the problem was/is intermittent, and (b) there is probably some performance cost to the switch (although it's not noticeable to me).