I don’t think I love my husband anymore

Well, goodness me, yes, but I don't think what you're experiencing needs to come under the heading of any syndrome. 

What you're describing is very likely similar to countless other women who have reached a very particular life stage. I'm guessing that you've most likely had a 'successful' marriage based on shared goals like raising the kids, managing a life together, dealing with life's ups and downs and basically getting on with it. 

Now, what you've grown used to is changing and its difficult and daunting in equal measure because you have no idea what changes like kids leaving to manage their own lives and onset of the menopause are going to mean for you. It's not surprising that in the middle of all that upheaval you are also questioning the validity of your relationship with your husband. 

Significant life stages and particularly those which happen in middle and older years prompt the "what do I want to do with the rest of my life". Taking a close look at a spouse and wondering what the next twenty years might be like is very common and probably quite a healthy thing to do. To my mind, it certainly needn't suggest that you no longer love someone, only that you're taking some space and time to really think about the future in as far as any of us ever can do. 

I think its a testament to the strength of your marriage that your husband has not dived into a seriously bad place because you have been honest with him about how you feel. Whilst it must be distressing for him, his counselling will hopefully support him to work with the current indecision about the future of the marriage.  

My advice is that you now do the same. See a counsellor, not your husband's, and work through how much of all this actually relates to him and how much is simply about you. Of course the two are intertwined but working with someone who will be neither guilt inducing or judgmental may provide the space to really explore which of your options feels right. 

If you decide to stay in the marriage I'd also strongly suggest that you both attend couple therapy. I have worked with many couples where one or both partners has reached an important milestone in their life which has caused what they thought might happen to become less clear. Counselling  would potentially enable you both to work together on how the relationship could better meet your respective needs and highlight those areas where compromise is the best option. 

Lots of people get to the stage you describe. The 'I love my partner but I'm not in love with them' and 'I feel close to and comfortable with my partner but I'm not really attracted to them any more'. These are all real feelings which can certainly encourage a good look at what may need to change in any relationship. They certainly don't mean that the relationship is necessarily over.