Sourdough starter does not really need refrigeration and so you can leave the sourdough starter out at room temperature for basically forever and it will be just fine.
However if you've previously refrigerated your sourdough starter then it's recommended to keep the sourdough starter in the refrigerator when not using it.
Sourdough starter should be refrigerated within 12 hours of using it if it's been previously refrigerated.
I always recommend to refrigerate the sourdough starter but you don't have too but it's a good idea to do so.
Also you should and do need to stir the sourdough starter before using it.
When you stir the sourdough starter before using it the sourdough starter will work better and have more flavor.
It's also recommended to stir the sourdough starter every few days or so even when not using it as it helps it maintain the flavor.
Sourdough starter does improve with age overtime and the longer you keep the sourdough starter the better the flavor gets.
However after about 10 years the sourdough doesn't get much better with age and there won't be much of a difference between 50 or 100 year old sourdough starter and the 10 year old starter.
Sourdough starter can be kept for many years without going bad and if you keep the sourdough starter for up to 10 years then the flavor improves.
But after the 10 years there's not much improvement in the flavor or much improvement in the sourdough starter itself.
But you can use very old sourdough starter and still get great results.
Most people use the sourdough starter well before 10 years but I've heard of some people keeping it for over 50 years.