It looks like the router is somehow broken. In the meantime I flashed the factory-file too. It works fine as long as the rooter is not rebooted. I can connect via ssh and after a reboot I cannot connect via ssh or luci anymore. What changed after the 2 flashings, is, that the port led shows on, if a cable is connected.
After the "factory-flash" the old password is still active. Isn't this strange? So could it be, that the flashing isn't done correctly?
Could it happen that No space left on device (no space left on device) made the router unusable? Actually it is no problem, I have 4 more TL-WR1043N/ND v1.8 and I will buy a C7 in the next weeks.