Important note: If I can still see part of the Firefox window, it keeps running as normal. If the program is minimized or obscured entirely by another window then it stops performing any tasks.

Slight correction: If I can see part of a Firefox window while another program's window is partly obscuring it then Firefox keeps chugging along doing what it's supposed but only if the mouse if hovering over that portion of the Firefox window still visible. Otherwise is stops processing like clockwork each time the mouse hovers over a different program window.