OK this is going to take quite some time to work out so the first step what settings are you playing these games at? Second are you using the newest driver or the ones that were on the CD? Is crossfire enabled or in single gpu mode? Is it possible that you could make a few screen shots or a short video of the symptoms?
Well since texture memory is dynamically assigned by drivers these days depending on the amount of system ram in installed. If you have less than 6gb of system ram or a very small page file or none at all could be a culprit.