All these answers are wrong about duration and lasting effects.
The standard duration of a potion depends on many factors. The example potion on YS281 is an very powerful thaumaturgic effect (pass through any barriers) in exchange for a very short duration. The default duration of a potion is 1 scene and I will expand on why shortly. First, why is the example 1 exchange?
"The thaumaturgical effect on this potion will provide 5 shifts of “sprinting” in a single exchange—including the ability to pass through normally impassible barriers, like walls."
Please take particular note of the part that says "including the ability to pass through normally impassible barriers". Because of this and the desired effect outcome the time is shortened to a "moment" (not an exchange). The distance is 5 shifts of sprint, but the effect is instantaneous as explained on YS265 under Duration and Enhanced Evocation and YS266 under Short-Term Spells. You sacrifice duration to lower complexity, allowing for powerful effects like "the ability to pass through normally impassible barriers". Exchanges are for evocations, the time table on YS315 is for thuamaturgic effects in most cases, including this one.
There is literally nothing that says that potions only work for 1 roll or 1 exchange by default. Again the default duration of effect is 1 scene. You can look at the list of example potions as a guideline also on YS303. Many of them specify 1 scene for duration. There is nothing that says you can only use it for 1 roll during that scene and that would not jive with how thaum works, thaum is not evo. Enchanted items replicate evocation and are reusable for stress in a very similar manner to rotes, potions replicate evocation OR thaumaturgy and are single use only.
If you make a potion that gives you a skill of +4 for 1 scene then you have a +4 on that skill for the whole scene. Saying that someone should use a stunt or enchanted item (which can only give you an evocation effect) is the correct alternative is not correct.
TL;DR Potions can give thaum effects and durations, and the default duration is 1 scene in most cases.
EXAMPLES
From YS303:
Bob’s “Love” Potion Duration: One scene
Red Court Antivenom Duration: One scene
Scent Suppression Duration: Several hours, or one scene if the potion is shared among two or three people.
Stimulant Duration: One scene
True Seeing Ointment Duration: A few hours, shorter if shared among two people.
From http://www.rickneal.ca/?p=654 (probably the best know DFRPG blogger):
Shadow Juice Duration: One scene
Bottled Confidence Duration: One scene