Can the Xbox 360 get updated more frequently instead of like once a month

Seeing as the 360 production was discontinued back in 2016 I would say it is very unlikely we will be seeing many more updates after the new xbox series x is released

Unfortunately, support for the console may soon be dropping off with the newest generation of Xbox consoles on the horizon for launch late this year. While it could be done, focus is put into where the majority of the player base is (as that varies over
time) the Xbox 360, as another use pointed out, is becoming dated. Support focus has shifted toward the Xbox One mainly and will eventually full on shift to the Xbox Series family of consoles in the coming years.

That's a tough question and it would need to go through Microsoft to get an answer. As the newer Xbox's come out I do doubt there will be updates but I am probably wrong.

It probably could. But honestly the console is a bit outdated now. The developers have the possibility of creating more bugs by updating it more often. You never know.

PlayStaion does have these issues. More frequent than Xbox. Never once can I remember Xbox Live being down for over a month, but PSN was down for a month and a half back in 2011.

Little do we forget the things in the past....