We have 9 japanese maples, all but one planted in the ground for about 20-30 years. There is always some dieback. Just make sure you clean your pruners(with bleach)between cuts so you won't spread any diseases, and cut back the dead stuff several inches into the good wood. You can always prune to even things up. We wish to keep some of ours less than 10' tall, so we do some MAJOR pruning every few years. As long as you have a healthy tree, prune it for the shape you like.

-Babka

I have Red Maples not Japanese Maples.

I know I saw my Dad just cut a maple tree nearly down one time and within a couple years the tree was nicer looking than before he cut it. Everybody said he killed the tree and was shocked that it grew back.

Same rules apply no matter what the nationality(!) of the tree. ;-) You can prune it anyway you like it, but a good rule of thumb is to not take out more than 1/3 of the tree at a time. Also, since you don't know the cause of the die back, clean your pruners after you cut that dead part out.