iMac will lose wi-fi connection but still show connected.

Which version of OS X? 10.7.x/10.8.x?

Wifi problems seem to crop up a lot on here and unfortunately there doesn't seem to be a 'one fix' solution.

However, sometimes any one of the following can help although, unfortunately, not always - in no particular order:

• Check wifi security - if it's WEP change it to WPA or WPA2 (preferably, as it's more secure)
• Change the wifi channel on the router
• Create a new Network Location: http://support.apple.com/kb/HT5289
• Reboot the router

Also take a look at this link and the links within the article for other ideas. They mainly reference Lion, but still seem to be relevant to Mountain Lion:

http://osxdaily.com/2011/11/06/lion-wi-fi-problems-solution-mac/?utm_source=feed burner&utm_medium=feed&utm_campaign=Feed%3A+osxdaily+%28OS+X+Daily%29&utm_conte n t=FaceBook

...and this link:

http://osxdaily.com/2012/11/30/resolving-stubborn-wi-fi-connection-problems-in-m ac-os-x/

I had this issue for months and my fix was to change the wifi channel. My router channel was set on auto, I change to manual and selected channel 9 and have no problem for several weeks.