Mathematica shuts down when calculating this limit

With

 $Version
 (* 10.3.0 for Microsoft Windows (64-bit) (October 9, 2015) *)

Mathemeatica returns a limit that depends on r, as it should.

Plot[Limit[E^-(r^2)^(2*n)*r*2*Pi, n -> Infinity], {r, -2, 2}, AxesLabel -> {r, Lim}]

Addendum

Although Limit returns unevaluated for arbitrary r, it can be made to produce useful results by making assumptions on r. For instance,

Piecewise[{Assuming[{#}, Limit[E^-(r^2)^(2*n)*r*2*Pi, n -> Infinity]], #} & /@ 
    {r < -1, r == -1, -1 < r < 1, r == 1, r > 1}]
(* Piecewise[{{0, r < -1}, {(-2*Pi)/E, r == -1}, {2*Pi*r, -1 < r < 1}, 
   {(2*Pi)/E, r == 1}}, 0] *)

which reproduces the plot above, apart from the discontinuities at r = -1 and r = 1.