Hi there, bridgesense!
Thanks for using the Apple Support Communities. Based on the information you provided in your post, I am understanding that Apple Music Radio doesn’t seem to be playing as smoothly as you expect; every so often it will stop, as if it’s buffering, and you’ll sometimes have to quit iTunes and reopen it to get the stream going again. I love listening to music, and Apple Music Radio is an awesome way to do that—I’m happy to help make sure everything is working as it should!
The first thing I would suggest is to restart your Mac by selecting the Apple menu in the upper left of your display and choosing Restart from the drop down menu. Once your Mac is back on, test Apple Music Radio again.
If it continues to pause and buffer after a restart, try restarting your modem and router as well. You can also move closer to the modem and router to see if that improves your stream, and I can also recommend that if you have multiple devices using the same network to try taking some offline while you’re streaming to see if it improves the connectivity.
The next step I would suggest if the issue persists would be to test your Apple Music Radio stream in new user account. The following article will give you some information on why testing in another user account can be helpful, and also provides steps to setting up a new account.
How to test an issue in another user account on your Mac
If you continue to have issue streaming, I would then recommend trying Apple Music Radio on another network, if possible.
Happy listening!