I'm 90% sure this is false. I once summoned Solaire for S&O (I was bored and wanted to make it harder). He died during the fight, and I then won. (there's a chance I'm remembering incorrectly and I summoned him in the Undead Parish to troll invaders and he ended up falling to his death around the bridge, and I then went and killed the boss; it was one or the other)
After that, I never saw any of Solaire's summon signs, and I never saw Solaire in body form (he wasn't at the Sunlight Altar, he never appeared anywhere at all in Lost Izalith, etc.).
Edit: they key difference is I won the fight after the phantoms died, rather than I myself dying as well, I know you can re-summon them if you die too.
Os iusti meditabitur sapientiam Et lingua eius loqueter indicium
Npc phantom death has no more affect on future availability than it does an actual player. They are undead just like you, and for all intents and purposes, their deaths are treated same way as yours.
In my most recent playthrough on ng+, Solaire died during the gaping dragon fight (who interestingly got buffed by the Chaneller up above because I just ran through most of the area). I killed the gaping dragon moments after he died & he was still available at Anor Londo.