Girlfriend wants to break up?

Hello, all.

I am the boyfriend of a fantastic woman (I'll call her "Jane") and we've been together for just over 6 years now. About 2 years ago Jane was diagnosed with triple negative, non-hormonal breast cancer. Since then Jane has lost most of her left breast, gone through a full round of chemo and radiation, was recently diagnosed with the cancer having metastasized in her sternum, and is now in a second round of chemo. On top of all this, Jane has several auto-immune conditions AND Type I diabetes.

Since the initial diagnosis, Jane and I have had sex about 5 times. Between the cancer and the auto-immune issues she has been incredibly fatigued. We were told her health wouldn't get back to "normal" for at least a year after the end of radiation, which was in February of this year, only a couple of months before this new diagnosis. While I've missed the sex a lot, our relationship has been very good.

Recently, however, our situation has been increasingly awkward and tense. Jane has been working on a project outside the home (which I support her in) and has sort of disappeared from me. She is working with friends and has thrown herself into that world entirely. About 3 weeks ago, it got so bad that I confronted Jane about it. She said that she feels we no longer have any "chemistry" and that we're really just roommates who call each other "honey." I was shocked because this sounded to me like I was being dumped and I reacted as such. We didn't speak for the rest of the night and the next day, still hurting, I sent an email saying that I would start moving out while she was away. She replied that she was not anxious to see me leave, and we haven't talked about it since. She has said that I should still feel that I'm welcome in the house and that she loves me. I don't want to leave her and have written a letter saying as much and laying out all my feelings about us. She hasn't responded to the letter yet.

Since the "break up," we haven't seen much of each other, but when we have it has been calm and cordial, although a little strained. We've spent nights in the same house with no problems, although NOT In the same bed. Jane has also been keeping her sister and parents at arm's length.

Now FINALLY to my question(s)! Is it common for people with cancer to distance themselves from partners and family? Should I take the "break up" at face value and leave? It would be very hard for me to do so, and I'm worried about what will happen when Jane's project is over and she has to come home to an empty house. Is it best to try to talk to her about the situation again, even though the letter didn't get much of a response?

Thanks for reading and for sharing anything you have with me!