Hello -
My understanding of the VI's is that they are working as intended. The VI's you are using demonstrate the concept of taking a random bit stream, modulating, transmitting, recieving, and demodulating. This physical layer process seems to be working exactly as expected. You may also notice that the message is only genated once in the original example and is continuously output (meaning that there is no noticable 'beginning' or 'ending' to the continuously streaming constellation.
Secondly I understand that you are introducing your own set of bits, which contain meaningful data. (unlke the random bitstream used in the original example.) For this type of data I recommend a more complex communications architecture using packets and error correction. The following example video and code provide one possible alternative framework for accomplishing this task.
Building an over-the-air link: http://zone.ni.com/wv/app/doc/p/id/wv-2757
Packet Based Link: https://decibel.ni.com/content/docs/DOC-18801
Using this framework will require some effort to dig into the code, understand the program, and make the appropreate modifications to handle the structure of your data, but I believe it may provide you a more satisfactory result.