I installed Mountain Lion yesterday and find that when my 2 year old iMac comes back from sleep it finds the router and connection but fails to allow internet connection. In other words it indicates the machine is connected but I cannot access Mail or use any Internet browser.
I have two PCs in the house that have no problems, so I assume the problem is neither with the modem or the router. There was never a problem when I was running Lion, it began only after installing Mountain Lion, so once again I assume the problem is with the new operating system. My iMac is circa early 2010. My son's iMac (2012) is not demonstrating the same problem. The most reliable way to establish an internet connection is to reboot my router (NetGear N300). When the computer reconnects after the reboot, it invariably finds the Internet. I have occasionally been successful Turning Wi-Fi off, and then back on, but most times not. I see that other users are reporting similar difficulties. Even if no one has an answer I hope that this is brought to the attention of Apple Engineers and a fix is quickly forthcoming.