Could you give us a rundown on what your procedure is prior to cutting? Is the wood clear coated in some way before the masking is applied? I typically take a hair dryer or heat gun to the masking as I am applying it to encourage the adhesive to stick. Or I let it sit out in the sun for a few minutes after applying it and then come back and press/roll it again.
I have had a lot of luck ditching the masking all together for certain projects (especially ones with a lot of fine detail or sharp points). So say I wanted to cut your same design and it to be natural wood color with blackened cut areas, I would try cutting the design with no “prefinishing” at all (and no masking) and seal it all with a clear coat after the cut was done and let it dry. Then I would come in with a small brush, black paint, and a wet rag. Dab the paint into the cut and wipe back the surface with the wet rag to remove the excess, which should come right off thanks to the clear coat/sealing. This method works well with wood species where the darker color will “bleed” into the surrounding wood fibers, as well.
Along with the other guys that reccomend a fresh vbit…I have found that certain types of Vbits cut soft masking better than others. So when I have a project that calls for masking + vcarving I always default to one of my Amana bits that uses carbide inserts instead of a traditional vbit and run them at around 20-21k rpm. Typically leaves no fuzzies at all.