Matty F wrote:

I assume that it's a 230v (thereabouts) AC vacuum cleaner, so there
should be a continuous 230v AC at the brush holders when it's running.

No, no, no - it will be a series wound motor and some voltage will be
dropped across the field coils. The heavier the mechanical load on the
motor the higher this drop will be.

The test suggested is still useful though. If the voltage across the
brushes rises when the motor cuts out it points to an o/c in the
armature (v. unlikely, IMO). OTOH if the voltage falls the intermittent
o/c is elsewhere. Use a test lamp (15 W pygmy bulb) or a robust old AVO
7 or similar. If there is an intermittent o/c you might zap your lovely
DMM with the multi-kilovolt spikes that will appear across the brushes.

IME the problem is more likely to be an intermittent connection in the
internal wiring of the motor itself (including the RF suppressor chokes)
- or the appliance switch even, or the flex. Intermittent breaks in
flexes subject to a lot of rough use are quite common. Give everything
a good tug or waggle while the motor is running.

--
Andy