So with befuddle, because the spell itself notes a duration (this being one round) the spell only lasts until the start of your next turn.

I like painful vibrations as an example, because its a "damage spell" without being a basic save, although it functions very similarly to one.

You'll note that different from Befuddle's spell entry, Painful Vibrations has no noted duration, because it is instantaneous. Your conditions that could be applied based on their save results have a specific duration in this case however, because they are separate from the damage done by the spell (which happens and ends during the spell cast). So in the case of painful vibrations, you cast it and they critically fail, you roll your damage, they become sickened 2 until they spend an action to retch (or some other mechanic to rid themselves of a point or two of sickened) and are deafened for 1 minute.

Where the same cast of befuddle still, no matter how badly they flub the save is still a 1 round duration no matter what. That said, despite it's short duration, it is extremely potent as a spell. Especially for it's cost when put on a staff. You, in that round, can capitalize on it much less than your allies can offensively, but it is also a great defense against a caster - though they typically have better will saves. Even if they get a success they are casting at a lower DC, lower spell attack and have a chance to just completely waste the spell they were casting.

EDIT: For an example of a longer-lasting Befuddle-like spell, look at Touch of Idiocy.