I think at that point Michael was very wary of who he could trust and Connie was one of those people (even if she went behind his back when he was in the hospital).

She did clean up her act from the woman she was in GFII and I believe Michael respected the fact that she came to live with the family and be with them (something Michael asked her to do when rejecting her lover).

I also believe Michael had a soft spot for her because of how Carlo treated her and the fact that she was introduced to Carlo by Sonny.