I don't think there is any "absolutely official RAW" reason this would work, but it is fair to justify it as follows.
You light the troll on fire while it is down and shift backwards to avoid burning (fair for this "light and move" to be a Standard Action, "improvised attack" imo) the effect of which is Ongoing Fire 5(save ends) and a 1 square zone of fire which does "If creature starts its turn in this zone it takes ongoing fire damage 5. If it already has an effect causing ongoing fire damage increase the damage by 5 and the target may not save against that effect (if a save would end it) this turn".
Thus starting its turn in the zone will cause it to increase its Ongoing Fire Damage (from the original lighting) to 10 and ensure it will kick in next turn = dead by fire = permanent. The net effect of this is, at worst, one round of stand up (with 10HP) and attack something in range atm then fall over at the start of next turn. So assuming the players don't stand next to the fire the net effect is stand up, shamble, die. As such just have it stay down.
Basically your DM should allow "hurt by fire while dead-ish" = don't get up. Especially as the property on the troll should really say "If not reduced to zero or lower by an attack that does acid or fire ...." or you can only keep a troll down by causing exactly enough damage to leave it on exactly zero. As this is nonsense, then reduced to less than zero should be allowed, so being reduced to "even lower" (from -10 to -11 say) shoudl prevent the reanimation imo.
EDIT : NInja'd - that will teach me not to be so careful with my wording (or just to proofread faster)