I have already tried it that way with LimeWire 1.3 and 1.4, and the only effect was that the existing part was deleted and the download began at 0% again.

Furthermore, I know well how you expect the Resume Feature to work, but I can tell you that it has never worked on my machine.
Normally, a transfer gets interrupted because the user on the other end killed the upload or disconnected from the net. a resume try will therefor have no effect at all. I have never observed that LimeWire actually was able to connect to another servent of that group and resume the file, even if there were 15 entries in the group.

And was I wrote was true: This question is posted over and over and I am not the first one who complained about not getting answers to it. (just look for old threads and you will see)

I have asked many limers an how it is done, and everyone told me that they never got a download resumed properly, just as i didn't., that's why i don't think that it is a fault of my system.