There is no easy or sure-fire answer. It's also not something that will be easy to hear.
The first step to take, is to talk. Are they saying this because they are unhappy with how your relationship is now? Is it because they are looking to other people and have interests in someone else?

Ten years is a long time, and you both have certainly changed. It's possible that you've grown apart or grown up, and they are feeling disconnected from you. With work and children, stress always will factor into a relationship.

If in fact, they are certain that the feelings they had for you are gone, then you need to take care of yourself. As much as we can love and want to be with that person, if they aren't feeling the same way, we have to let them go. Holding on and tormenting yourself will end in disaster. It always does. You need to find your self worth and your strength. Regardless of where they go, you need to find your own direction. Just because you are no longer traveling life's adventure with them, doesn't mean your own adventure stops. You are simply taking a different road. And most times, that road leads to something much better.

Yes, you will miss them. Yes it will be hard. And yes you will blame yourself. You'll want to beg them to stay. You'll most likely cry for quite a while.
But then, you have to continue living. Focus on experiencing life, and making an impact for yourself.

You have loved, and you have lost. But you have not failed. Failing at love is only never trying. Think about it like this. If you knew 10 years ago, that they would leave 10 years later, would you still have gotten married? Would you take the 10 loving years, knowing that it all will be gone? I would. Yes, it is best to love, and lose, then to never have loved at all.

After talking you may also find that while the passionate "in love" stage is over, their "out of love" feelings are due to a distance between you, for whatever reason.
As a couple, you must ALWAYS make time to be a couple. Without the kids, the household stress, and other similar factors that cause many couples to "grow apart". Sometimes we become comfortable with our spouse, and stop trying, stop the compliments, the thank you's, the kindness and actions that were shown in the beginning of our relationship.