I had an interesting situation come up the other day. A player was casting Suggestion on an NPC, who succeeded on their Wisdom save. Since the spell didn't work, the player immediately cast it again, this time successfully convincing the NPC to do the thing. This seemed a bit weird since the player could theoretically cast the spell again and again until the NPC rolled sufficiently low. Is this allowed RAW?
Yes, it is allowed by RAW
When the designers want to restrict an effect to one use per X time, they say it explicitly. Take the following abilities from the Monster Manual, for example:
Luring Song, from Harpy
[..] A target that successfully saves is immune to this harpy's song for the next 24 hours.
Or this one:
Charm, from Succubus/Incubus
[..] If the target successfully saves against the effect, or if the effect on it ends, the target is immune to this fiend's Charm for the next 24 hours.
Or this one:
Frightful Presence, from Ancient Black Dragon
[..] If a creature's saving throw is successful or the effect ends for it, the creature is immune to the dragon's Frightful Presence for the next 24 hours.
Suggestion does not have this specific clause, so you can use it on the same target until it fails its save.
Casting a spell takes around 6 seconds. That's enough time to react
A full Cast A Spell action, which is what casting Suggestion takes, takes up your entire turn, meaning to complete it, it takes around 6 seconds. Even if the NPC could be targeted by a second casting of this spell, they have another 6 seconds to react and to avoid it. They shouldn't just stand there waiting until the spell is finished casting.
Otherwise, it's like they are saying "I punch the NPC" and then missed, and then they say "I punch him again!" until they kill the guy. The NPC shouldn't just be standing there waiting to get hit. The first time they targeted him, he should know he isn't in the presence of friendlies.
Casting Suggestion on someone can be considered a hostile action
When your player used Suggestion on that NPC, you should have considered that a "surprise round" for the purposes of combat. Following that, have them all roll Initiative. This gives the NPC a reasonable opportunity to escape, call the guards, etc., assuming he is able to beat the PC's initiative. If he doesn't, then it's justified that the PC is able to cast a second Suggestion before the NPC could react.
...but the target will remember both suggestions, which might go badly sideways for the caster
A spellcaster can keep casting suggestion on a target until they run out of spell slots. But if it doesn’t work the first time, what’s really going on gets a lot more obvious.
Consider this guidance about suggestion from Sage Advice:
Some spells are so subtle that you might not know you were ever under their effects. A prime example of that sort of spell is suggestion. Assuming you failed to notice the spellcaster casting the spell, you might simply remember the caster saying, “The treasure you’re looking for isn’t here.
Now imagine you had succeeded on their first save, and the caster made the same suggestion again.
You will remember the caster’s suggestion, and that you disregarded it as preposterous — but the second time he said it, suddenly you agreed. This “Wait, what?” moment can change your whole perception of events.
Your DM may rule that your nonsensical reactions makes if easy for you, or your companions, to discern that you have been bewitched.
From the example, if you fail the first save, you probably just go look for the treasure someplace else. If you fail on a subsequent attempt, it’s a lot more likely you will become highly suspicious, or even recognize the caster has tricked you (probably with a successful Insight check) — even though you are convinced the treasure is elsewhere.
If you know you are being forced to do something, you can work against the spirit of the suggestion in all sorts of creative ways.
There is no inherent limitation to re-trying Suggestion. However, since it's a level 2 spell, trying it multiple times is costly and doesn't guarantee a good outcome before running out of slots.
It should be noted that whether it is success or not, the caster must always voice the suggestion to the target. Targets with a good understanding of magic might realize they're possibly being targeted by a charm and take countermeasures or become hostile. This option makes the most sense for characters who are experienced mages themselves, or deal with them frequently.
Yes, but note that the Suggestion is required to sound reasonable to the target. If you have cast a Suggestion, and failed, making the same suggestion again would not be, or sound, reasonable. So, yes, you could cast it again, but you'd have to suggest a different course of action that would still sound reasonable to a person who had heard and disagreed with the first suggestion.