Hi Cultrarius,
Thanks for your very good input!
The trail is using WorldSpace. When I tick LocalSpace, the trails are not visible anymore, I wonder if/where they get rendered.
However, when I disable the LWC support… the trails do not reset anymore! 
Problem solved? I wonder what is going on under the hood.
I also found out a very weird detail: the “LWC Support” is not displayed anymore in the Niagara panel:
However, when I specifically search for it, it appears:
Problem solved?
Might switching off LWC support cause larger issues?
From a short testing, everything now seems to work.
So the bottom line is: in order to make Niagara work with LWC we need to… choose the option NOT to support LWC?
I will update again if there are further issues generated by this workaround 
Thanks! 