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PFS' downtime rules require such a buff to last through the entire downtime period.
Ultimate Campaign's Downtime rules don't seem to have such a restriction, but it would be a perfectly reasonable add in my opinion...
You are not allowed retries on a professional skill to earn income. But can do so on an attempt to accomplish a particular task. That indicates that earning income is actually a single roll not a series of rolls. The fact you are rolling further reinforces this point. If it was a series of rolls the results would average out and you would end up with an average score. Since you have a chance to fail horribly or get an incredible success that would indicate it is not a series of rolls.
Neither of those abilities have any time limit on them other that it only applies to a single roll.
You are running a mythic game and you are worried about a character earning some extra gold?
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Somewhat depends on exactly what downtime rules you are using. For example if you're using the Kingdom-building rules and this player is the Treasurer, then they can't use Display of Wisdom. The Economy check is not a "wisdom-based skill check or wisdom ability check."
Other than that it's a little bit up to the GM.
For general-purpose "I'm performing a skill to earn income/craft/etc." my personal ruling is that you can use any spell that 1)You know or can prepare every day, 2)Has no expensive material components, and 3)Lasts at least 8 hours when cast by you. I also allow any non-spell abilities that apply "when a roll is made" such as Display of Wisdom, Inexplicable luck, or an Investigator's inspiration. Even if they use up a resource such as mythic power or inspiration, as long as that resource refreshes daily at no cost.
Other GMs may feel that such abilities aren't usable. Their logic is "even though you only make one roll per day it's representing continual work, and you would have to be under the influence the whole time. You don't have enough mythic power for that." I don't agree (one roll is one roll), but it's not irrational.
Display of Wisdom (Su): As a free action, you can expend one use of mythic power to attempt a feat of Wisdom, gaining a +20 circumstance bonus on one Wisdom-based skill check or Wisdom ability check.
Benefit: Once per day, as a free action before a roll is made, you gain a +8 bonus on any single d20 roll. You can also use this ability after the roll is made, but if you do, this bonus is reduced to +4.
I can understand not allowing something like Owls Wisdom with a stated duration that is less than the time period required to make the skill roll, but neither of those abilities have a set duration. The only limitation Display of Wisdom has is that you have to spend a mythic point. The limitation of Inexplicable Luck is it can only be used one per day.