Of course, I don’t know why they didn’t just say…
“Also, once per round, it takes radiant damage equal to 3 + your Charisma modifier when it makes an attack that doesn’t include you as the target”
That's easy.
Let's take an example where The initiative order is striker, paladin, enemy.
Round X: The paladin Divine Challenges (DCs) the enemy and attacks it (ensuring the mark does not expire before the paladin's next turn). On the enemy's turn it attacks the striker. The DC inflicts damage.
Round X+1: On the striker's turn the enemy either gets an OA or uses an interrupt against the striker. Under the current wording DC cannot damage the enemy, since the paladin hasn't had another turn since the last time DC did damage. However, under your proposed 'once per round' wording DC inflicts damage again, and can not inflict damage again this round. This means that when the enemy gets their main attack later this turn there is no longer the threat of damage from divine challenge hanging over them to deter them from using their more powerful attack on one of the paladin's allies.
So changing the wording can change how effective the power is as a deterrent.
Hm... I can kind of see that interpretation. You're saying that "your next turn" means the paladin's next turn after the victim takes radiant damage, rather than the next turn after the mark is applied. And that the "Also" is meant to attach the radiant damage clause to "While a target is marked", rather than to "You mark the target". Which is somewhat supported by the paragraph division. Interesting! I find that now that I've looked at the text that way it's hard to not see it that way.
No, you're confusing the rules for duration with the rules for how often damage can be applied. Nothing in the duration rules mentions next turn.
Here are the rules for how long the Divine challenge remains on the target. (Quotes taken from the D&DI Compendium)
You mark the target. The target remains marked until you use this power against another target, or if you fail to engage the target (see below). A creature can be subject to only one mark at a time. A new mark supersedes a mark that was already in place.
"Next turn" isn't mentioned. In fact, turns aren't mentioned at all.
The next paragraph is the the rules for the damage: (truncated to avoid copyright infringement, I hope. The removed text pertains to the amount of damage.)
While a target is marked, it takes a –2 penalty to attack rolls for any attack that doesn't include you as a target. Also, it takes radiant damage equal to ... the first time it makes an attack that doesn’t include you as a target before the start of your next turn. ...
This is the part we're arguing about - whether this is recurring damage throughout the encounter or not. Playtester experience and reports from DDI say it's recurring damage. The first attack part is, I believe, there to indicate that the paladin cannot choose which attack triggers the DC damage - it's always triggered on the first 'infringement'.
And here are the rules for engaging the target, mentioned in the first paragraph as being necessary to maintain the effect. Note that here we have rules regarding the paladin's
current turn.
On your turn, you must engage the target you challenged or challenge a different target. To engage the target, you must either attack it or end your turn adjacent to it. If none of these events occur by the end of your turn, the marked condition ends and you can’t use divine challenge on your next turn.
So if a paladin ends a turn without either having attacked the DC'd target or standing next to it, the effect ends. If the paladin has DC'd another target, they have to also attack or end up next to it instead, and the first target is no longer marked or under the other effects of DC.
Oh, and since the power is not 'Sustain: Minor" we know the paladin does not need to re-DC the marked target each round.