Thank you for your response. I experimented a lot with moving the devices around, connecting both wired and wireless but nothing made any difference. However I am not sure if I tried local files, I usually use it for radio and Spotify.
Regarding your last remark, it is the LMS on Max2Play that causes the trouble, independent of what kind of players I use (Squeezebox Classic, PiCorePlayer, Max2Play…). Now that I am using the LMS of my Daphile again, all problems have vanished.
And remember: the trouble starts when I use more than one player at the same time. It seems this is too much load for the LMS on Max2Play, although the web interface is very responsive!