This is a recurring theme I hear from people all the time. I don't want other people "stealing my__________" clients or candidates is usually the most common response. But think of this. This all stems from a fear of loss a lack of approval, security and or control. Here are some other ways to overcome this fear.
A) Grow your network. A larger network as a whole is much less about the individual connections and more about the depth of the network. It relies more on quality can be found in quantity theory and offers the added benefit of "screening" hiding valuable relationships.
B) Make sure you keep those relationships solid by staying in communication. Recruiting is and has also been about relationships. Ourclients don't use us because I'm the cheapest they use us because we have a relationship with them and they trust we can get the job done.
C) You can't loose something that is not yours. Evaluate the actual "relationship" do you only call that customer to talk shop or do you also make it personal build rapport and a more solid foundation?
D) Not accepting invites does NOTHING to stop someone from seeing your connections. Say you take a stance that you are NOT going to accept invites from other recruiters, but the guy in the cube next to you who you are connected to (or anyone else in your network for that matter) does accept the invite, guess what they can see who you are connected to. There's a block on the right column called "How you’re connected to" which shows you all the potential ways you are connected to a person. OK fine you just (in effect) moved them to your "second level" but they still have full access to your most important connections because I guarantee you others are not taking that same stance and they will be able to reach that connection via another connection. So who's network are you really stopping( that's right your own)
Now though I accept all invites I must admit that I do NOT forward all requests. Example I had a candidate ask me to forward a resume of a candidate to a client for a position which I was working on with the client. Yea obvious conflict of interest there. I can't take money out of my own pocket. I simply replied to the candidate that I had a conflict and that I couldn't forward.