Some of my Facebook friends have run into a problem when other people want to “friend” them. Their “Friend” button is gone or disappeared. The solution is really very simple. This is a setting controlled by you in your Facebook security settings.
To get your “Friend Me” button back, just click on your Account Tab (Far top right in Facebook), then click on Privacy menu item, then “Edit Settings” beside “How You Connect” – change the drop down on “Who can send you friend requests?” to “Everyone” and click “Done”
Take a look at the screen snap shots below for a graphically view on the process.