Tom,
What Robert is asking is if you selected your input from the input dropdown (when the raster is in the map) or if you browsed to the raster on disk. This may make some difference is older versions. However, I just tested 10.0 sp1 and in both scenarios I am returned a 4 band result. I ran the Clip tool located in Data Management Tools > Raster > Raster Processing and the result was also 4 bands. The Clip tool can clip to feature geometry just like Extract by Mask. Give that tool a try.
What version are you using?
Regards,
Eric