Put simply, Chris Baird is not a defensive midfielder and doesn't have the legs/stamina for it. This is shown when he's played there and has looked pretty terrible. It's not surprising that at his peak with Fulham he was a wing-back and that's where he looks best now, especially with the organisation of Pulis.
In this respect he reminds me of Steven Reid before he got too old, and that is a pretty good compliment as Reid was decent here for a few years.