Sure, I'd be happy to help you with that. Here are some steps you can follow to resolve random playlist playback issues on YouTube:

1. **Check your Internet Connection**: A slow or unstable internet connection can cause issues with playlist playback. Try to refresh your connection or connect to a different network and see if the problem persists.

2. **Clear Cache and Cookies**: Sometimes, your browser's cache and cookies can cause issues with YouTube. Go to your browser's settings and clear your browsing data, then try again.

3. **Update your Browser**: Make sure you're using the latest version of your browser. If not, update it.

4. **Disable Extensions**: Some browser extensions can interfere with YouTube. Try disabling them one by one to see if any of them are causing the issue.

5. **Try a Different Browser**: If none of the above steps work, try using a different browser to see if the issue is specific to the one you're using.

6. **Contact YouTube Support**: If all else fails, you may need to reach out to YouTube Support for further assistance.

Remember to also check if the "Autoplay" feature is enabled on your YouTube. If it's not, your playlist might not play continuously.

I hope these steps help you resolve your issue! Let me know if you need further assistance.