I assume you're talking about the two bolts that attach the stabilizer bracket to the cylinder head, and not the ones that attach the stabilizer link to the bracket. If so, the double nut or nylock nut won't help in that case. It would if you were talking about the stabilizer link to bracket bolts however.
I can't think of many reasons for the two bolts into the head loosening that easily, other than damaged threads in the head that are pulling out or possibly bolts that are bottoming in the holes before the bracket is pulled up tight. Screw them in by hand without the bracket until they bottom and measure the distance from the head surface to the underside of the bolt head and washer. Compare to the thickness of the bracket and spacer. If the bolts are bottoming too soon, get shorter ones or add a thicker washer to the originals. Clean the threads in the head and on the bolts thoroughly with solvent, apply high temp thread locker, and reinstall.
If the threads in the head are slowly failing and pulling out, I guess the fix would depend on warranty status and what you're comfortable with.
Jerry