The symbiont is already 300 years old by the time of DS9. Just how much longer can it continue on? Obviously the death of Dax would mean the current host would also die since they become one after a short period of time.
We know that Dax can easily live at least another 200 years (happy and healthy in Children of Time) and probably a fair bit more as there is no mention of them reaching severe old age.
No one, even on the Trill home world, made any mention of the Dax symbiont as being particularly old. Seems like she probably has plenty of centuries left, as long as she stays away from crazed Cardassians.
In Trek Lit, specifically The Worlds of DS9 vol 2: Trill Unjoined by Andy Mangels and Michael A Martin, the Trill symbionts are noted to reach ages exceeding 20,000 years. However, at some point before 2,000 years of age, they get too big to continue life as a symbiont within a host and return to the Caves of Mak'ala where, over millennia, they can reach a length of about thirty metres. So, theoretically, Dax could live to be over 20,000 years old if you like the idea. If one prefers to stick to canon, at least 550-odd years as @Tosk points out, or approx. 1,750 years old according to the New Canon of @The Wormhole
It isn't an age limit, per se, so much as a limit on the number of incarnations. They can handle 12, unless they get some transferred to them by another Trill in a Christmas special, season premiere, or season finale.
Do you think at some point there could just be too many memories to handle? I feel a headache coming on just thinking about having five people’s lifetimes all buried within one mind, I can’t imagine 12 or 15. I think it would just be too much.
Nah, you just forget stuff to make room. Plus, the host doesn't automatically have access to every memory previous hosts had, or even all the memories of the symbiont.
Didn't Ezri have trouble with exactly this? Although I don't think it would be that bad to be honest, you don't simultaneously remember every memory you ever had all at once.
I've always thought that Dax could be a bridging character in a Trek series set in the far future from the 24th century. Of course, Data in a retooled body (i.e.: different actor) could do the same thing.
Yeah according to the novels the symbiont can live for tens of thousands of years. Though one joined to the host probably can't live 20,000 years. I expect the Dax host-so long as the symbiont survives could indeed live that long and have countless hosts over millennia with knowledge and experience building off of knowledge and experience. As I understand it the Dax host was relatively young-having been around for maybe 200 years. So it has a long life ahead of it.