Did you install urxvt from the Ubuntu repositories? Which package? Or if you compiled it yourself, what compile-time options did you use? What features did you enable?
If you've installed via the Ubuntu repositories, try installing the rxvt-unicode-lite package instead of rxvt-unicode. The lite version is compiled with many of the extra features turned off, and may solve your problem without digging into all the various options.
urxvt aka rxvt-unicode has a lot of prettifying features built in. More than likely you're seeing a problem with one particular feature, and disabling it will fix your problem. In particular, try removing transparency/libAfterImage support, Xft fonts, and ... I don't know what else.
See the urxvt(1) man page for a list of runtime options. These jump out at me as good things to try turning off:
-rv - Turn off simulated reverse video; resource reverseVideo. -tr - Turn off illusion of a transparent window background; resource transparent.-depth - use a bitdepth that matches your X-server-fade 0 - turn off fading-on-focus-loss
See the urxvt(7) man page (and urxvt FAQ) for a list of compile-time options (bottom of the page). If you've compiled your own, try compiling a new version with the --disable-everything option and seeing if that helps. If it does, you can add features back in and try them until you find the one that's causing the problem. In particular, these options turn off things that I'd expect to be sources of trouble:
--disable-transparency--disable-afterimage--disable-fading--disable-frills--disable-swapscreen--disable-xft
