Repairing a pixellated drop-shadow gradient

I have inherited a vector PDF and an SVG file of a logo made from 
outlined letters with a gradated drop-shadow (see 
http://xml.silmaril.ie/downloads/letterlogo.png for enlarged PNG fragment).

When the logo is enlarged (eg for use on a poster), the drop-shadow 
shows up pixellated. Both files exhibit the identical problem. When 
edited, the drop-shadow is indeed made up of pixels. I assume in my 
ignorance that it was passed through some software at some stage in its 
past which concretized the drop-shadow as graded pixels.

How would I go about removing the drop-shadow entirely, and replacing it 
with one of identical color and extent, but done in such a way as to 
withstand enlargement without deterioration?

Peter