If Klaus1's advice doesn't help...
Make a New Location, Using network locations in Mac OS X ...
10.5, 10.6, 10.7 & 10.8…
System Preferences>Network, top of window>Locations>Edit Locations, little plus icon, give it a name.
System Preferences>Network, click on the little gear at the bottom next to the + & - icons, (unlock lock first if locked), choose Set Service Order.
The interface that connects to the Internet should be dragged to the top of the list.
For 10.5/10.6/10.7/10.8, System Preferences>Network, unlock the lock if need be, highlight the Interface you use to connect to Internet, click on the advanced button, click on the DNS tab, click on the little plus icon, then add these numbers...
(There may be better or faster DNS numbers in your area, but these should be a good test).
While I have not created a new account, this Mac has two: one for the end user, and my Admin account. Yesterday I logged in as Admin, and surfed the Internet to see if the issue presented itself.
Oddly enough, it did. I then switched back to the User account expecting Internet access to be disrupted. It was not! Eventually I did get the issue to occur for the User account as well. Then I had to log out of both accounts in order to reestablish Internet access.
Finally finished testing a new Location, which does seem to have helped this issue.
However, a more infrequent issue seems to be more prominent. This Mac is getting errors that it is "unable create a secure connection" to secure (https) sites!
Hmmm, check System Preferences>Network, unlock the lock if need be, highlight the Interface you use to connect to Internet, click on the advanced button, click on the Proxies tab, what is set there?
Also, are you running in a Managed, or Admin account? Parental Controls enabled?
In Sys Prefs>Security>Firewall, what is allowed there to connect?
Are you running any Anti Virus or web safety software?