My 85 vanagon has developed a problem where the engine won't crank at
all when the starter battery voltage has dropped to about 1/2 charge
or around 12.0 volts.   When you turn the key, there is a "click" and
you can hear the voltage drop a little, but the starter doesn't move
at all.  I've verified this behavior with two different batteries,
and checked all the battery connections.

Is this a known failure mode of the starter or starter solenoid?

Thanks!