It happened to me yesterday, changing the proxy settings doesn't fix the problem.
My account is logged in via fb. What I did was, I logged out and logged in again, this time on the spotify log in fields with the same primary email of my fb account, the `No internet connection ...` is gone and I can stream again.
I've worked as an IT technician since 2002 and this problem drives me crazy with this app. I occasionally get this issue on Windows computers and it seems to have no rhyme or reason or method that always fixes it. I've been a paying customer for several years, but Spotify, you really need to fix this issue with your program. Whatever method the program uses to determine if it has a connection to the Internet, doesn't work very well!