Seasonal jobs that might turn permanent - 15 weeks in

A staffing agency says some roles convert to permanent after 8 weeks. I have read a lot of threads here and could not find my exact situation. I would like to avoid a gap in my résumé. Has anyone been converted to permanent?

Thanks for writing this out. I went through something close to it last year, and it got easier once I kept a simple log of every call and form.