I noticed that the sattelite lib script stops the propagation of click events on a button if the network request to the analytics server is not successful. Unfortunately some ad or tracking blockers block the analytics domain so this happens quite often.
In that case things like the hamburger menu stop working. When I remove the analytics script from the page everything works fine.
The solution was to remove the Adobe analytics script until our operation guys could add the necessary CSP headers in production.
The call that stopped the events from propagating was the first call to the analytics subdomain of the main site. The script made another call to secure-ds.serving-sys.com which failed as well (it was blocked by the CSP headers). But that didn't break the site.