Internet stops working only on my Mac mini

A couple of times day or more now the conection on my mac quits working while everything else on the network works fine. You can shut off Safari and restarted it to no avail, and refreshing does nothing. Switching to the cat5 line doesn't work ether, nor does turning off and reconnecting to the wi fi. The only thing that works is restarting the computer. Whilst this is only a guess, I think maybe some kind of flash program is trying to run and is stealing all net fuctions.

Other then that guess I've no idea.