Does a character hit with Drow Poison always have to attempt the 2nd Fortitude Save?

The description of Drow in the SRD states:

An opponent hit by a drow’s poisoned weapon must succeed on a DC 13 Fortitude save or fall unconscious. After 1 minute, the subject must succeed on another DC 13 Fortitude save or remain unconscious for 2d4 hours.

Does the character have to make the second saving throw if they succeeded in the first save? The inclusion of the word “remains” suggests that the character was already unconscious, which suggests that this second saving throw is only required if the first one was failed.

However the rules for poisons suggest that the second saving throw is “usually” required even if the first succeeded. But it talks about additional “damage” which unconsciousness isn’t, exactly:

When a character takes damage from an attack with a poisoned weapon, touches an item smeared with contact poison, consumes poisoned food or drink, or is otherwise poisoned, he must make a Fortitude saving throw. If he fails, he takes the poison’s initial damage (usually ability damage). Even if he succeeds, he typically faces more damage 1 minute later, which he can also avoid with a successful Fortitude saving throw


If a character succeeds in their initial saving throw against Drow poison, are they still required to make another save a minute later?