Thank you for your suggestions, Joe and Anand.
Meanwhile I found out the cause (I post it for everybody else
encountering a similar feature):
I had set the screen size explicitly (as opposed to using frame.pack())
and also used the method BorderFactory.createEmptyBorder() with
fixed numbers (for distance from top, left, bottom, right) for some
gui elements.
On a screen having height=1024, width=1280 the gui looks fine,
but on a screen having height=768 and width=1024 my buttons got
invisible because of the fixed createEmptyBorder: the
given numbers were too high on a smaller screen.
(By the way: this is how to find out the user's screen size
Using frame.pack() made the buttons visible again, or,
using different numbers for creating empty borders for
different screen sizes.
(How to solve this in a elegant way is a different chapter, though)