I had the same problem years ago. I installed a sump pump in a below grade barrel under a grate at the bottom of the stairs. I suppose an alarm would also be nice, but the pump completely solved my flooding problem. This is not a cheap solution, but it removed the stress of worrying about the leaves and melting snow every year. I also lowered the grade outside so that the concrete (and grate) were about 4" below the basement grade.
