Is it true that sinus problems are permanent? Or can one be fully treated and cured even after having ongoing problems with congestion

This is not true. Sinus disease is actually not the same in every situation. Milder sinusitis is much more "curable". For instance, obstruction of the maxillary sinuses alone is much more curable than obstruction of all of the sinuses (maxillary, ethmoid, frontal, and sphenoid) with nasal polyps. Also, identification and management of allergies contributing to the sinus problems greatly improves the "cure" rate.
Sinus Cures. Sinus issues can be caused by a number of factors - often more than one. Allergies, bacteria, viruses, funguses, a deviated septum, foreign bodies, gerd with naso-pharyngeal reflux, nasal fractures, cystic fibrosis, thickened secretions that can't drain and immune problems (a partial list). See an ENT doc to sort it all out and discuss your options.
Sinus disease. Many commercials lead one to believe that all facial pain is sinusitis. Not all nasal obstruction is sinusitis nor all patients with findings on imaging like MRI or ct has the disease as well. There are many good treatments for nasal obstruction and facial pain and even sinusitis but you should find an otolaryngologist and neurologist you trust and seek their opinion about the cause and rx for you.