The current FAR/JAR requires a positive lateral gradient with sideslip - the aircraft must roll and the stick must go laterally to trim a side slip. Also, the pedal must trim to a new pedal position that supports the sideslip. Since helos are hover machines and have no natural gradients in a hover, there is a speed where the rules are no longer met, the aircraft is flat in its response to yaw, and for most helos it is 55 to 60 knots.
This is based on airplane flight characteristics. No helicopter has any natural roll with sideslips below about 55 to 60 knots, so no helicopter can be IFR certified below those speeds, in spite of autopilots that do all the work.
Also, the longitudinal static stability must be positive at Vmini, but this is seldom the reason for the current 55 to 60 knot Vmini.
I disagree with Shawn, many helos allow IFR flight below Vmini with good results - every SAR approach is an example. I have flown perhaps 200 approaches with a DGPS coupler to a hover, all very nice and all without a care about obsolete FAR requirements.