Esther,
Unless you added code to manage multiple connections, this is the expected behavior with the example you mentioned. Once the first client connection is made, the server is no longer listening for additional connection requests.
For an alternative example that demonstrates using a queue to keep track of any number of client connections, look in the same example library but check out "Multiple Connections - Server", along with "Multiple Connections - Client 1" and "Multiple Connections - Client 2". These examples used to be named "Date Client" and "Date Server" in earlier LabVIEW versions, and while they have never been fully updated to use the native LabVIEW queue structure, they demonstrate old-school (and perfectly functional) LabVIEW 2-style globals.
If I've understood your problem description correctly, you will have to make modifications to your VI so that it does something similar to this. If I've misunderstood, then please reply with more information (What do you mean "the second message is not accepted"? Are there errors produced? Could you attach your VI? etc.).
Regards,
John