Hey gang! 
This one may already have an answer somewhere but darned if I can find it.
Running an OotA Paladin and in the interest of having a one-handed ranged attack (Shield Master, always want to keep it equipped), I grabbed 5 darts. Was going over my spell list and noticed that Ensnaring Strike will work with thrown weapons, since it doesn't specify melee only, nifty! Then I looked at Elemental Weapon.
Nothing in the RAW says "you have to maintain contact with the weapon or the spell ends" like some of the other weapon enhancement spells (ie, Shillelagh), you just have to keep concentration. "For the duration, the weapon has a +1 bonus to attack rolls and deals an extra 1d4 damage of the chosen type when it hits." The "when it hits" is my question. If I throw a dart at something and hit, it would then (to my mind) be lodged in the target. Its not like a bullet moving at supersonic speed, and even with +3 STR I don't think I'm punching holes in people. So technically it has "hit" but also maintains constant contact with the target. That being the case, wouldn't it continue to deal the elemental damage component unless the target yanked it out or something ended the spell?
For example, take the stuff of my nightmares: black puddings. You enchant the dart with fire and nail it. 1d4+3 piercing, plus 1d4 fire damage. Since the weapon is now magical, it doesn't dissolve (per MM). Wouldn't it continue to deal the magical part of the damage since it is A) still a magically flaming dart and B) still "inside" the creature?
Or even simpler: toss a lightning dart at a thug, it sticks. As long as the spell is active wouldn't it still be pouring juice into the guy?
Mechanically it would be a once-per-round 1d4 damage (not sure when though, maybe if it isn't removed by the end of the monster's next turn?), and at PLD Lv. 9 (when we get access to EW) there are probably a lot of different ways to deal out much more carnage, but in a pinch when you don't want to get close but still want to contribute to damage, it seems like a neat way to do some ranged DoT, especially if the target has a specific vulnerability.
Or does this all boil down to "it doesn't re-hit, so no"?
Thanks in advance!
I wouldn't let you continue to get the damage, no. Basically because it doesn't rehit, as you say. I'd picture the damage as a burst of energy on a hit, not a continual emission. Otherwise how would you carry the thing? You'd be getting shocked yourself.
Because magic? 
But seriously, it just seems odd to me that they wouldn't specifically limit it to melee and yet make it a waste to use anything else, especially for the cost of a level 3 spell slot. You'd basically need a Dwarven Thrower or the Weapon Bond trait to get your weapon back to throw again to hit again.
Oh, and while we're on the subject, what happens if a Monk catches your magically enchanted weapon and chucks it back at you, since the text reads "when IT hits", not "when YOU hit?"
I would totally allow someone to enchant and throw a dart for continuous damage. Rather than OP, this actually seems either easily countered (pull the dart out, throw it back at the paladin) or very situational (get it stuck in a slime). The rules imply no such thing happening, though.
As for the monk thing, yeah. Just as they'd get the benefits of your magic item if you chucked it at them, if they acquire your temporarily magic item, they can use it against you.
I suppose you could always drop concentration in that instance since you can do it at anytime and it doesn't require an action. But there goes your spell slot for basically a cantrip's worth of damage.