Ok, I checked my debug settings and recognized that I had chosen the hex output file for debugging. With this file functionality is there, suspend and resume works, but debugging is not possible. But if I'm chosing the out file (two times bigger, with -Xelf option) for debugging, even functionality is not there and resume does not work. I guess it's a format problem. I'm even wondering, that there is no .elf file as I know this from older projects with another tool chain.
I set the -Xelf linker option, so I would expect that output should be in the right format. Is there somebody who is able to successfully debug with GDB and DIAB?