steve and tangent, here's the rub with TI,
to weld TI you must be meticulously clean, have strict attention to preventing weld puddle contamination, and MUST purge both the inside and outside of the tube to create an inert (read oxygen free) weld zone. Anything less than perfection is sure to result in fractures at the point of contamination due to the molecular structue becoming brittle and less ductile.
Common errors in welding TI include imperfect pre-cleaning, tungsten contamination, moving too fast (outrunning shield gas), improper torch angle (gas not shielding area appropriately), and lack of inert gas due to improper purging.
Sooo, given this info...
I would not reweld the chainstay as it would be impossible to clean the interior of the tube sufficiently and purging would also be an issue. If you would try, with much riding, the weld zone would likely fracture again. As for the other side...the tensile strength and ductility of TI is awesome when joined correctly, unforgiving when not. Hard riding will seldom cause a failure (could...) but more likely if one side failed, it is likely the other will as well.
Steve, these concepts also illustrate why riding a copped steerer tube is NOT a good idea. Even with a lap butt, too much probability is present in inability to prepare the tubing and shield the lap during welding to meet my expectations of a strong joint. I'm not going to send someone out on my work unless I'm confident they'll bust their ass before my fork
Hope this helps...