One eye floater that won't go away. Is it a problem to always remain there?

Not likely. Many people have a persistant single floater. As long as you have had it chacked out and there is no evidence of a retinal tear or detachment, then a single floater is a minor annoyance and will not cause you any problems. Always be alert to any change in your floaters, as that copuld be a sign of a new problem.