I think they say about 95% of cases end up with at least one refinement stage, but three is the max I've heard of except in very rare cases. I looked it up and only three refinements are included in Invisalign Express, just like with Invisalign Full.
From what I understand, the Invisalign Assist is for providers who don't have much experience with the product. Ultimately Invisalign is based on computer models and the human body doesn't always respond the way the model does, even if you're perfectly compliant with wearing them. I think those orthodontists who have done a lot with Invisalign have a good idea of what will work and what won't and how to manipulate the product to get the desired results. I get the impression that with the Assist product the provider is very limited in the changes they can make to the ClinCheck, so they're kind of at the mercy of the company.
I wish you the best of luck... hopefully 4th time's the charm!