Hi Ambimind - the problem is that the curve is not closed, if it was a closed curve, the object type indicator in the upper-right corner would say "Closed crv" when it was selected, but instead it says this:



So saying just plain "curve" there as the object type means it is an open curve - in order for trim to work the curve needs to be closed so that it fully divides the surface into different regions.

If you extrude it you can more easily see the open area:






EDIT: AAhh, Danny beat me to it! :)


- Michael