How about this possibility:
When the elves fled Xen'drik it was a time of chaos and it was pretty much a case of "grab whatever you can lay your hands on and run." As such, the elves have a whole bunch of arcane knowledge they've never really properly examined, or got misfiled during the setting up of their new home. Included in their grabbing are the seeds of the planet-damaging spell that brought the dragons down on the giants.
The elves don't know this however, and since the Aerenal are generally conformists rather than innovators, they don't make the leap of reasoning needed to put the seeds together. But, every once and a while, some elf does make that intuitive leap, and the dragons' mystic sensors pick up a specific 'ping'. Then, it's off to 'war'.
The dragons use the cover of the war to find that particular elf and wipe him/her out, along with their research. The chaotic nature of the fighting has so far kept the Undying Court unaware (or are they?) of how close they have come to unlocking something that would bring the whole wrath of Argonnessen down upon them.
The dragons only fight long enough to make sure the research is stopped, then lose interest.
Of course, an opposing idea, that the dragons only attack the elves as part of scholarly debates to test out different theories of the Draconic Prophecy adds a certain amount of deliciously sick irony to the whole war.
"Hmm. I'm not sure the evidence backs up your theory."
"Well it's either two more centuries of careful experimentation and rereading vast conflicting tracts of the Prophecy, or we can go hit the elves and see what shakes out."
"I hate lab work. Let's roll."
Or worse, the dragons' attacks are merely them going for take-out between centuries-long debates.
"You feeling like Tairnadal, or Aerenal tonight?"
"Aerenal. Those Tairnadal horses give me gas."