The issues I had with sinew lifting off the limb were due to improper surface prep. I've done 2 sinew bows since then using hide glue on both and both are doing fine.
My new prep method is to degrease by scrubbing with Dawn dish soap and rinse with boiling water just before adding the sizing and then the sinew. The hot water and soap "wets" the wood so it absorbs the glue into the wood and not just on the surface.