I found the answer of this question in this blog post by bhageera.
In the end the reason was pretty silly… the counterparty I was connecting to allows only 1 connection per user/password (i.e. session with those credentials) at a time. As it turns out there was another application using the same credentials against the same TargetCompID. As soon as that application was killed off, the current one logged in fine.
In my case, two clients with the same credentials were active on two different test environments.