I have a client who used to do this all the time. She has now pulled it back to twice a week - one is her weekly newsletter, the other a promotion about a product or workshop. She always gets unsubscribes, probably a good 10 or 12 a week, but she gets between 20 and 30 signups a week and her list is 5,000+ strong so I don't think she worries.
Personally I stick with a monthly newsletter for mine and if any of my readers want more, they sign up to one or more of my blogs. I do have a few 'fans' out there who enjoy my writing