The text of the Limp Lash spell is very clear on what happens if you hit the target, but what if you don't? Does it remain in play in your hand, much like some other touch spells?
Spell is lost if initial attempt fails.
Ranged touch attacks cannot be held unless the spell says so.
Limp Lash states that it's a ranged touch attack:
You must make a ranged touch attack with this spell. If you strike your target, he takes a 1d6 penalty to his Strength, Dexterity, and Constitution each round. This penalty cannot reduce any attribute to less than 1, and once any of these attributes reaches 1 the target collapses and his body, except his head, becomes paralyzed. While paralyzed in this way, the target retains full use of his senses, including the ability to feel pain, and can speak (including casting spells with only verbal components). The whip has a maximum length of 20 feet, 15 hit points, and a hardness of 5. The spell ends immediately if you let go of the whip or it is destroyed. When the spell ends, all penalties the target took from this spell also end.
PFRPG core rulebook page 186:
Ranged Touch Spells in Combat....Unless otherwise noted, ranged touch attacks cannot be held until a later turn.
Notice the "Holding the charge" (page 185) italicized section which is after the bold "Touch Spells in Combat", which makes this section look to apply only to non-ranged touch spells.
The caster gets but one ranged touch attack with the spell limp lash
Despite the spell limp lash requiring the caster to make a ranged touch attack, making a ranged touch attack is different from casting a touch spell. The caster of the limp lash spell can't hold the limp lash spell's charge—even if the ranged touch attack is unsuccessful—because the spell creates no charge to hold! (Also see Duration on Touch Spells and Holding the Charge and Cast a Spell on Touch Spells in Combat.)
That is, because the spell limp lash has the entry Range: 20 ft. instead of the entry Range: Touch, the spell limp lash functions as per its description, requiring the caster to make a ranged touch attack against a creature when the spell's cast, and, if the caster misses, the spell just ends.
An aside: Keep the peace by not using the spell limp lash
There are probably worse written official spells, but I'm unaware of them, and I've written about some goofy spells. As written, if the caster succeeds on the ranged touch attack to hit the target, the target suffers a cumulative "1d6 penalty to his Strength, Dexterity, and Constitution each round" (minimum 1) and when "any of these attributes reaches 1 the target collapses and his body, except his head, becomes paralyzed." A target's spell resistance must be checked, but there's no saving throw. In other words, the spell's hilarious(ly powerful—O, my!).
However, what happens between the affected target's first round and the affected target's second and later rounds is, as written, anybody's guess. It takes the limp lash spell's entry in the FAQ to explain that if the caster or the affected target are separated by more than 20 ft., the spell ends, even though that's not how a spell's range usually works. Likewise, explains the FAQ, if anything breaks line of effect between the caster and the affected target, the spell ends, which is also not usually how a spell's range works (q.v. Aiming a Spell on Line of Effect). But that's what the range of this spell means, specific trumping general via the FAQ.
But the spell also lacks an effect entry (q.v. Aiming a Spell on Effect), yet the spell creates something—a "dark whip-shaped field of energy" according to the flowery description—and that thing has hardness and hp. This omission makes this reader cringe. In addition, the spell's flowery description mischaracterizes the spell's effect, saying that You create a [whip] that wraps around an enemy’s neck, leaving everything except his head paralyzed until you let go of the whip or it is destroyed. This only adds to the confusion the spell creates—like if the spell fireball were prefaced with This spell leaves your foes' charred bodies littering the battlefield or whatever: sure, that could happen, but that's the best case scenario! (Most level-appropriate foes caught in fireball spell instead just say, "Knock it off!" and stab the wizard.)
Finally, there's no actual duration for this 2nd-level spell. If a foe can be first rendered unconscious, the foe can—at the cost of a lone creature capable of employing a scroll of limp lash (2nd-level spell at caster level 3) (150 gp; 0 lbs.)—be taken out of action indefinitely unless the foe's capable of casting spells with purely verbal components (like the spell dimension door). Hence, a nonnative outsider, for instance, could cast the spell limp lash and effectively secure a prisoner forever. And while that's interesting, that seems a bit much for a 2nd-level spell.
More can be read about the limp lash spell—and the questions it raises and controversies it causes—in these messagboard threads from 2012, 2012, 2012, 2013, 2014, and 2015; really, such threads are pretty much all over the Web. This GM recommends other GMs consign the spell limp lash to the scrap heap alongside spells like aboleth's lung.