I replaced the reed contact, but this did not change the situation
That part of your post seems odd.
Yes, the glass-embedded reed switches can, in rare cases, get permanently stuck in the "on" position, i.e. the two reeds fail to separate, even after the magnetic force is removed, but would that happen twice in a row? It's highly unlikely, unless the reeds in your replacement fried from over-voltage.
Choosing the right replacement reed switch rated for the proper voltage (Neumann does not sell it, so it will be aftermarket) and paying attention to precise installation of the fragile glass enclosure is crucial, for the reed/magnet combo to properly work.
Here is what I would do:
1. remove the head from the mic
2. remove the magnet switch
2. measure continuity of the reed element (it should be open, but if both reeds look stuck together under a magnifying glass, examine whether you chose the correct reed switch for this application)
3. re-install the reed element to the precise height of 1.0 mm off the base, and make sure it's soldered in perfectly level with the base.
The precise distance between reed and magnet is crucial to make the contacts work properly when sliding the switch in and out of range.
Good luck!