You can't get them to respond if they do not want to.
If they are not active they are not going to respond and if they are active it is already a response. A response is not always an answer to your messages or mails - it can simply be the fact that they are active.
What you can do is to be the best sponsor you can possibly be and give them every opportunity and way to respond to you and to become active or if they are active to ask for your help should they need it.
Keep on encouraging even if you do not get the desired response - maybe after a while they will start responding.
I think we all have to deal with that feeling that you are communicating with yourself or wondering if you are wasting your time trying to reach them. Maybe you wonder if they are even receiving your newsletters or reading them. Don't let that get to you - if you do your best it is good enough - it is them that is failing themselves - you are not failing as a leader.
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You can't get them to respond if they do not want to.
If they are not active they are not going to respond and if they are active it is already a response. A response is not always an answer to your messages or mails - it can simply be the fact that they are active.
What you can do is to be the best sponsor you can possibly be and give them every opportunity and way to respond to you and to become active or if they are active to ask for your help should they need it.