4th failed demo in a row. What can be done?!

Thanks Vincent

You are right. I'm trying to determine which other aspects (maybe more soft skills oriented?) can I envisage to enhance the situation... Today I'm kind of "far" from the team and I participate almost only in demo...Maybe I should get "closer"...but I do not want to step-in the scrum master role or add more chaos...

Don't you have reason to be on-site for a few days? then make one so you get a feel of floor.
Or what about being present virtually to daily meetings?

Above all, might need to wipe the slate clean and get back to the basics. Pare down the next sprint considerably. Help the team create something they can truly achieve, after so many failures morale will be low. While forming complex plans and communications is great, if you have time, what you need is to address the crisis you have on hand. Get your best, key people involved, identify the issues in the sprint retrospective, and tackle the next sprint with less tasks, better written stories, etc. Of course, get permission from your leadership to go nuclear on it. Get tough, get real, and get leadership on board with your plan to get the project to rights.

You mentioned that the Scrum Master was nominated. Have your Scrum Master and Product Owner been trained on how to run and participate in Scrum? Has the rest of the team?

It was also mentioned that the stories might be too large. How is your team sizing the stories? Is your team accepting stories into a sprint that are too large to be completed in one sprint? Sprint Planning is your last chance to catch Epics and break them down into stories. The team should be asking questions about and sizing each story before it is added to the Sprint Backlog. Do you have a clearly defined Definition of Ready that has to be met before a story can be included in a Sprint?

Has your team established a velocity they are able to maintain?

I'm not sure what you meant by "a paternalising organisation will tend to take time to investigate how it could be solved." The nature of Scrum is to experiment and to learn from the experiments. One of the tenets of Scrum is to fail fast and learn from the failure, not to keep repeating it. If something is not working, it should be addressed in the sprint retrospective. A new approach should be identified during the retrospective and used in an upcoming sprint. During the retrospective where the new approach is used, the team evaluates how well the approach is working and decides to either continue or change.

These are just some thoughts, without knowing more about what your team knows or how it functions. Hopefully it helps.