I don't know how this has happened, but the log window has disappeared.
Whenever I run UDK with the log window turned on, I see the log window flash momentarily but then it vanishes.
I can still minimize it and I can maximize it, but in its normal state it doesn't appear anywhere on either of my screens, kind of like it were told to appear somewhere beyond the bounds of my screens.
I used to keep it at the top of my second monitor. I haven't changed my screen settings or the location it appears at. It's just... gone...
sometimes it likes to go away into the left, out of the screen. shift + right click the program in the windows taskbar, select 'Move', then press any of the directional keys in the keyboard (up, down, left or right) then move the mouse without clicking anything. this will get you the log window back
however every time you run the game it will go away. the way I found to make it stick to that position you tell it to, is to do the same thing but in the editor instead of the game. then both the editor and the game should have it in the last position you moved it to