The problem went away after a firmware update of the Performers’ router.
The funny bit (well, not so funny after all) was that I could connect successfully with both partners, either as engineer or with the Performer application, while the two of them couldn’t keep a connection active for longer than a few seconds. You never know…but when the router/firewall has such problems, there is not much we can do. So the advice is to keep your firmware up-to-date.