Having the same issue, details:
I was in the middle of a custom game trying to see how Vi played and what not. After about 4 minutes of play the game started having the reconnect issue come up.
Several minutes of trying to reconnect, LoL crashed out.
I restarted LoL and got a message asking me to Reconnect to a disconnected game.
If I click on the orange Reconnect button it lags until it tells me my turned off firewalls are causing connection issues.
If I don't and simply close out and try to reconnect same issue comes up.
I tried deleting the file as stated on page before this one and it did not work.
It's frustrating, but I'm sure it will be fixed. Sucks though since I got off work early enough to play a bit and apparently fate decided LoL is not in my future right now