Your suggestion to update DirectX 9 does nothing, sorry.
This is an engine-level problem which has existed for years, and has been widely reported by users. It was originally identified as a "memory leak" though this is probably an inaccurate description of the issue. BioWare claimed that it would be fixed in an update, but it never was and instead patch 1.05 only ever brought fixes to DLC authentication issues.
Basically, the game will run fine for the first 10-20 minutes, but after a while performance will begin to tank. Framerates don't drop much, but loading stutter is introduced, such as when opening menus (inventory, skills, journal) and when in conversation with NPCs. On top of that, the game will persistently hitch and stutter for a split-second evey few seconds, which is most noticeable in conversations but can occur in regular gameplay too.
This problem is significantly gameplay-harming but at this point in time I highly doubt it will ever be fixed. The only "solution" is to save and restart the game every time the performance degrades to a point where it becomes annoying, anywhere from 10-30 minutes on average.
