I tested this issue in DNN04.09.04 , I can add contact person. My steps are as follows,

 

1. Register one new user called "test1","test3"

2. Login to DNN as user "admin" , then open cute messenger, and add "test1" and "test3" as contact person

3. Login to DNN as user "test1", and add "test3" as contact person.

 

What's your DNN version? You can send your site url and detailed reproduce steps to [email protected], I will test it.

 

Regards,

Eric