This is the server side error - this message is generated and send to you be the server. All ImapResponseExceptions indicate errors returned by the server.
Is there any limitation in Limilabs for parallel connections
There are no such limits in Limilabs Mail.dll. It is the server that is rising this error, not the client dll.
I don't think you get this error after you invoke Idle method. Most likely it happens during the login - without the stack trace, or logs it's just a guess.
There is a good chance, that the server doesn't allow multiple (or so many) connections, you create, from the same IP address. You'll need to contact the server administrator to get the information. why the server raises this error.