This is normally caused by your Firewall blocking osu! traffic, or general networking nonsensicality.
First I suggest making sure nothing from osu! is being blocked in your firewall.
Secondly, give everything a good restart. Your PC, Router, Modem, the whole lot.
If nothing changes or you prefer a more direct approach, try releasing and renewing your IPConfig from cmd prompt, and Flushing your DNS
(If you need help doing these steps, Google can explain faster and better than I can here.)
Please post if any of these steps helped.