It really depends on a lot of factors. The most important thing is that people sign up for it and you let them know what to expect when they do.
I send out a main newsletter once per month - that includes my entire business because I have a website and eBay store as well as Etsy shop. That is my big mailing list.
Then I have a niche mailing list which I send out 3-4 times per month - a quick notice that special paintings and prints will be available at a certain date and time. But the number of people on that list is much smaller and I know they look forward to receiving it. I would never mail the big list that often.
If you have good content that people will look forward to read, then you can send it once per month. You are right that you have to be careful not to turn people off or tune them out. You don't want to just pitch, pitch, pitch. You want to offer something of value to them. If people tell you they enjoy your newsletter, that is a good sign!