Why did she toss me aside?

Love, Heartbreak

I met my lover 5 years ago.  We spent a lot of time together, and had a lot in common.  We went horseback riding, sailing, to museums and other points of interest.  We are both tyro writers, and attended a writer's group every two weeks - maybe that should have been my first hint - she didn't want them to know we were together.  She didn't intro me to her family, except to her sister; no invites to important events in her life, like when she changed positions (big deal - from one organization to another), when her father came out to work on her house (something I know how to do, and she deliberately kept me out.)
Just before my birthday she told me she couldn't see me any more - "I have issues," she said, but won't tell me what the issues are - today she told me that I loved her and she didn't love me, and that's why she wouldn't stay together.
Anyone else been through this?  She says she still wants to be friends, but not lovers.  She's asked me over to her house repeatedly since the 'breakup', and we keep ending up in bed.  So what's really going on?

A long-time friend tells me I should cut her off without another word.  What do you think?  Am I stupid to want to stay with her and keep trying to salvage the relationship?