Thanks again kmac.
Below is the description of the multiple exposure mechanism from the XE service manual. From here - http://www.suaudeau.eu/memo/manuels_rep/reflexes/minolta/xe_service_manual.pdf
You're right and I think there might be two possible places that need checked. The first is the film advance cancellation spring (3055) to ensure it's correctly attached. The other is the multiple exposure operation lever (3059) - under the film advance lever (under the top plate). This is visible in your exploded diagram - the black/dark grey thing at the front left, from which the grey, rounded metal multiple exposure axis (3054) protrudes (downwards and with a couple of bends in it, just above the strap lug). Looks like the ME operation lever is screwed onto a brass post. Reading the manual, when the ME rewind plate (0314) is engaged and moves the ME lever (0350) back to its start position, it disengages the ME lever from the ME operation lever but there appears to be nothing else - other than the film advance cancellation spring - to act on the ME operation lever to move it back to it's start position. That little spring is being asked to do a lot of work, not only returning the film advance cancellation lever (0170) but also the ME axis, which runs from the base of the camera to the top, and which then moves the ME operation lever. Any stickiness between the ME operation lever and the brass post would make things a whole lot harder for the spring.
I'll check the spring first. But I'll need to remove the top cover (film advance side) to check the ME operation lever. May be a few days before I can find time to do that but will let you know how I get on.
Thanks - Ian