A few questions, although this sounds perhaps a bit like a support issue.
Is your SSO a custom implementation? If so, you need to make sure that it doesn't protect the /api resources.
Standard Jive cookies and/or HTTP Basic should be used to access the API in Jive 6, and if you are protecting the /api resources, this could be causing the issues you are experiencing.
Hope this helps,
First of all, thanks for your help.
Regarding your question, the answer is YES. We have a custom implementation.
What I found yesterday, and maybe is something obvious for people that understand how SSO works in this environment, is that if I delete the jive.security.context part of the cookie, the problem is instantaneously reproducible. So, maybe the trouble comes form that part. But..... when I looked for that string in the entire code of our site and the jive 6 source, I couldn't find results. So, I'm still lost in the space.