Answer: In my experience these are in fact very difficult to root. (That is one of the reasons the majority of Japanese maples are grafted rather than on their own roots.)
According to James Dirr's Manual of Woody Plants, 6 to 8 inch softwood stem cuttings should be taken in July, wounded, treated with a strong rooting hormone, and stuck into a peat and perlite potting mix. They should be kept under mist until they have rooted (this can take months) at which point they should be left alone to undergo a normal winter dormancy or should be set under supplemental light and encouraged into active growth.
To be honest I have never seen mention of root cuttings for maples; this technique is generally only successful with nongrafted plants which tend to sucker naturally. Good luck with your project!
Q&A Library Searching Tips