Computer "timing out"?

I'm having a problem w/ my internet surfing and e-mail.  As I am doing either, within a few seconds, the page (or e-mail) will, for lack of a better word, "goes to sleep".  The blue title bar on the top of the page goes grayish blue and I have to click my mouse for it to become active again.  I can clearly view the page.  This will happen even if I'm actively typing a message.  It reminds me of what happens when you set a screensaver to activate if the computer is unused for X amount of minutes, except it is happening to me while I'm actively working. 

 

(It happened 3 times while I was typing this question.)