Hi Paul, thank you for your answer.
I think that this problem started after the last T4 framework update. JA Purity IV still always the same, no new update, so maybe the problem is not coming from the template.
So ok, you enabled the "Shared Session" in "Global Conifuration" to skip the frontend authentication when you already logged-in from the backend. This issue is really weird...
What's the issue with SP Simple Portfolio? Why do I need to keep the current version? Is because of the open_basedir settings that are too strict?
Thank you for your help