I told the apple employees exactly what is going on. That is every time I put my desktop to sleep and reopen it, I must go through the Network Diagnostics routine in order to access my wireless connection to the internet.
I have read of a number of people who upgraded from Snow Leopard to Mt. Lion experiencing the same problem. I followed a suggested fix in one of the user forums. This consisted of: entering system preferences, choosing the network icon, pulling down "edit locations", adding a new location and giving it a name and clicking done. The machine responds by returning to the Network screen. I then clicked Network Name menu and "join wireless network". According to the instructions that should have fixed the problem.
They suggested that, if it did not, I should renew the DHCP lease via the Sys Pref, Network, Advanced, TCP/IP Tab and verifying that the IPv4 was set to "Using DHCP". Then I was told to click on "Renew DHCP Lease" and to click apply when prompted. It was also suggested that I reset the MTU size to 1453.
I did all of that twice before taking my desktop to the Genius bar. The Apple employee rushed through various menus and pull-downs, etc. and announced that the problem was resolved. I tried to get him to explain what he had done but could understand about half of what he said. I took the machine home and turned it on and the exact same problem occurred.
I have even read on line that some users who upgraded from Snow Leopard are so dissatisfied that they are looking for ways to "deinstall" Mt. Lion. I don't want to do that. I just want this "glitch" fixed.
Any suggestions would be welcome. Thanks.