This seem to be exactly the same question as Laptop VGA monitor (ati card) blanks ~every 30 seconds, but since that question is closed, I have to ask it again and hope for the better.
My HP 8510p has a ATI Radeon Mobility HD 2600 card (RV630) and worked flawlessly with fglrx driver on 12.04. However, since the proprietary fglrx driver is no longer updated for RV630, it cannot be used with Ubuntu 12.10 or 13.04. Upgrading from 12.04 means switching to the open-source driver.
However, this driver does not work with external monitor (in fact, I have the same problem with the 12.04, 12.10 and 13.04 Live CD, so the driver must have been broken for a while; fglrx works). The external monitor goes blank, and the screen occasionally flickers and shows the Unity desktop for a couple of millseconds.
radeon.new_pll=0 to the kernel (or in
/etc/default/grub) solves the problem with the screen blanking, but resolution is limited to 1280x1024 and internal/external screen can not be configured individually. I don't know exactly this does, but I assume it disables some dual-screen features of the driver.