Hy,
it seems, that calling the support has brought the Solution.
Maybe it is interesting for other users, if this problems occurs.
The cause of the problem was the activationfile, which is on windows located in C:\ProgramData\Camera Bits, Inc\Photo Mechanic. (The folder ProgramData is hidden by standard)
The Solution for me was to blow away this file, start Photo Mechanic with "Run as Administrator" and do the activation again. Since I have done this, the Problem has occured no more.
If another Programm changes this file, changing the modified date is enough, Photo Mechanic maybe will be deactivated too.