Not sure what you can do about the timing out issue, as it could be a couple of things. You could always try using another IRC client (that is if you are using the on-site mibbit web client), that could be an easy solution. Other than that it could be your internet or simply (and obviously) your connection to the server. As far as I know there is nothing I can help with there.
As for your nick being connected still, there is a way to disconnect it easily. Explanation: the IRC server sends a 'ping' to you every so-often at the same interval (usually something like 30-90 seconds depending on the IRC server's configuration) to see if you're still connected. If your IRC client (for example, the mibbit chat) doesn't reply to the ping the server has sent, it'll think you are not connected, therefore disconnect you. The amount of time between your actual disconnection and when the server may realize you are not connected is the time your nick remains there. You can wait about a minute for it to disconnect automatically, or, you can register your nick which comes with a few security benefits along with the one I'll tell you about, which is a kill command to disconnect any nick you've registered.
If you just type '/ns register password e-mail' into the mibbit chat while replacing password with a desired password and e-mail with your e-mail, it'll register your nick for you. Just remember the password. When you connect you can '/ns identify password' to 'log in' (commonly just called identifying yourself).
Now here is the bit that will come in use for you here: /ns ghost nick password. Replace nick and password with the corresponding credentials and your ghost nick should disconnect.
// Those other benefits are also the fact that it makes it harder for other to impersonate you and stuff, people can't steal your nick.
I hope that wasn't too much info... I just like to be informative where I can be. If you want to take up using a different client I can always help with that too, just message me on Skype or MSN - I know I have you on those two and I'd be happy to help you set something up!