I think it very much depends on whether the redesign is just a UX/UI "refresher" or if it actually completely changes the way the service works and how you use

I think it very much depends on whether the redesign is just a UX/UI "refresher" or if it actually completely changes the way the service works and how you use it. I am thinking of Digg here which is a good example of a redesign that led to a significant outflow of users.