I had the problem below, and found this answer on this site...tried it and it absolutely works. 

When this happens, click the right-most button on the Home tab of the ribbon and select Sign out of Windows Live Mail. After a few moments, the default contacts list should load (it may be empty). When it's done so, click the same button again and sign in with your Microsoft Account. The account contacts list should load again; now try adding or editing a contact.

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My issue was:

All of a sudden in my Windows Live Mail (Windows 10) I can't add contacts.  I enter or edit the information and it tells me: "The contact information could not be saved.  Check the contacts information and try again".  I already had this contact and have written them many times but had xx in front of their name so I wouldn't send jokes, etc.  I tried removing the xx, I got the message...I closed and went back in. . . clicked "Delete this Contact"...same message.  Closed again, went back in and tried adding them without the xx...same message.  It's also done this on a friend who changed her email - same routine...message, etc.  Can you tell me what's going on.  I've shut down and rebooted till I'm blue in the face.  I would hope someone could help here because in trying to go to the support site that's suggest, I get a page telling me it's not available.  I feel this wastes valuable time and frustrates me and anyone else that has this issue and needs an answer that helps us get it solved.  If someone has a solution, would you please post.  Thanks so much.  Anna