How long xbox 360 servers is open?

I think there has been no announcement of the xbox 360 servers being shut down. As long as the 360 Games BC you can play with your 360 Console online

Can't underestimate how many are still possible using 360 servers, i'd give it a few years yet before anything like this happens.

I do not believe because there will be backward compatibility and shutting down servers would be a problem.

Seeing as the next generation will be backward compatible with previous generations, i would suspect that the 360 servers will still be available. That is on Xbox side atleast.

Game developers on the other hand will let the community and Xbox know if they are planning to shut down the servers for their games.

Unfortunately, no one can give a definitive answers since nothing has been announced yet. At this point it's just speculation. Personally, I don't think they will close right at the start of next-gen, especially you'll still be able to play the 360 games
that are already backwards compatible on the Series X. I'd imagine it will be more of a case by case type of situation where developers decided to shut down their servers for a particular title because it costs too much to keep them going for a couple people.