I finally nailed this after much searching.

This particular machine has a Kenton MIDI retrofit installed, and as it turns out, they way the power was being supplied to the MIDI board, it caused the whole MIDI board ground to have a slight 100 Hz (twice the mains frequency in this country) ripple superimposed on it. That in turn would be superimposed on the bend CV driving the bend/modulation panel, which then caused the oscillators to 'warble' ever so slightly. It's almost inaudible, at least you don't notice it until you know it's there.

Since the OB-Xa does not disconnect the bend lever during autotune (try bending and hit AUTO for some interesting fun), that meant that the pitch simply was not stable while the machine was trying to autotune, causing the resulting tuning to be rather random. In the BEND NARROW mode, it would work much better though, and since that function comes up randomly when switching the machine on, it would sometimes tune nicely and sometimes not for no appearent reason.

Re-routing the power supply to the MIDI board cured the problem, the machine now consistently autotunes fast and correctly. Pitch stability seems ok after an all-night soak test. Pitch accuracy could still be better, but I'm putting that down to the Oberheim design for now.

/Ricard