Is Xbox Live service terminated on Xbox 360?

Hello Di, this is Manuela. I'm an Independent Advisor and community user like you, ready to assist with this.
Not a Microsoft employee.

The Xbox Live network is still supported on Xbox 360 consoles, however, some games have been shutdown their servers.

We can try to sort this out. For this purpose, please answer the following questions:

Are you seeing this message in a specific game, or what are the games affected?
If the message is appearing on the Xbox interface, what are you trying to do before receiving this message?

Hello DI. Microsoft didn't announced something related to the Xbox Live on Xbox 360, so you don't need to worry about this.

However, we can try to solve this problem. Before starting with troubleshooting steps, may I know if you tried some procedures to fix this?

Thank you Manuela. I ran Xbox live connection test many times recently, but every attempt ended in failure. I posted the question online asking gamers who own Xbox 360 console and some gamers replied that they encountered the same problem. Some gamers who own Xbox one or Xbox series said that the Xbox Live on those consoles was running normally.

The information above makes me believe that the Xbox Live service is no longer available on Xbox 360. But I'm not 100% confident about that. So, I asked the question on the forum. The message you gave me put my mind at rest, thank you very much.

When Microsoft terminates Xbox Live support for Xbox 360.

I have 2 accounts. My first one was tagged to my original Xbox when XBL first went live back in 2002. When I bought my 360, I started a new Xbox Live account just for my 360.... When MSFT terminated the Xbox Live service for the original Xbox, I migrated
that account to another 360 I had purchased for the family room to use with Kinect and Netflix.