Hello Colin and Arno,
Because it worked in test (wamp) and not live, I looked further in the settings of jdownload.
What I noticed was that in the Configuration/Downloads area 4 directories where missing and therefore not writable.
So I added these directories manually and change the settings to 775 (writable).
After reloading the component they showed up as writable.
Testing to create a zip file (multiple files) worked perfect.
So this post is fixed.
Thx very much for your comments so far.