To be honest, I have not encountered that particular problem in my perimenopause. I have had enough other ones, though, to make up for it. But am glad that I still basically have the desire. I just had a surgical procedure recently and sex and everything related is off-limits for the next month for me, and I am having a hard time with it.
However, my OB/GYN is fantastic, and would likely take an issue like loss of desire seriously.
I think you should find a GYN well-versed in mid-life female issues so that you could rule out anything physical.
It is also possible that there could be a psychological issue ongoing, and if your GYN thinks that they could potentially refer you to a sexual therapist - somebody who specializes in sexual issues.
Have you had any other symptoms other than the lack of desire? Because after having so many hormonal issues over the last year or two, I can honestly say that if your hormones go wonky you usually have some nasty indication - especially in your cycles. If your cycles are still churning along normally, then I'd be surprised if it were hormonal, but I guess it shouldn't be dismissed unless it can be checked out.
Lack of desire can have many, many causes. Here's a list of some of them for you to think about so you can consider all of the possibilities in attacking the problem: Female Sexual Dysfunction