Well i have an idea, if the object is basic…
Say you have a circle filled with colour…for this example, red. Create another circle and put it behind circle1, then make a new colour swatch. Make the swatch a gradient set to radial, then make one colour red (for this example since circle1 is red) and the other white and make the white have an alpha value of 0. Now, fill circle2 by dragging with the paint bucket tool, from the middle to the edge. Delete the line from circle2 so you just have red fading to nothing. You can go back into the swatch and move the red further to the other side (on the slider thing) to create a sharper fade rather than a softer one.
Of course this only works as i said for simple objects. For a complex shape that wouldnt work at all, in that case im sorry i cant help.