My daughter, Lisa did not have Asperger's Syndrome, but she was much the same as your daughter. My heart and prayers go out to you. Lisa would hook up with an undesirable man for anywhere from six months to a couple of years. Eventually, she would realize she had made a bad choice and come home, only to repeat the pattern a few months later. It broke my heart and there were many fights and tears. I finally learned all you can do is love her and reassure her that you will always be there for your daughter no matter what. It is very hard to standby and watch, but if you want to be there for your daughter, you must bite you tongue and repeatedly tell you love her no matter what. Whatever you do, don't make her choose between you or him, it strengthens his position and she will always choose him over you.
As you may have noticed, I refer to my Lisa in the past tense. She moved to heaven about four years ago. At least I know where she is now, who she is with and that no low-life can take advantage of her anymore.
You and your lovely daughter will be in my prayers. Your other children sound wonderful. Enjoy your life, love your family and know that your daughter will come home to you when the money runs out and he gets tired of her, which is usually the case.
I hope I have given you some comfort in knowing you are not alone.
D.