Some news here:
In the meantime I have tested this with another Surface Pro 3 - an i7-Version.
The problem did NOT occur on that device!
So we still do not have a solution, but I have seen and tried a SP3 that works as supposed.
So eventually there is a chance to fix that behavior.
This is even worse news - did some devices somehow escape this flaw in manufacturing?
Why are most devices experiencing this but some aren't? If some devices aren't experiencing this, does that mean that Microsoft will see most devices as defective? Are they even going to bother to address this?
Are you sure you tested correctly?