Not quite sure I fully understand your problem but it sounds only natural that slack gets in the line as the minnow swims around and/or wind or current moves the float causing slack to get in the line. Dont know which bobbers you use but you might want to give pencil floats (even some weighted floats) a try. I rarely fish by casting minnows under floats and letting them sit for long, but when I do I usually try keeping most of the slack out as the cork moves by slowly taking up a little bit of the slack WITHOUT actually pulling the float.
Health nuts are going to feel stupid someday, lying in hospitals dying of nothing.