The "Berry Cycle" is actually different for each berry.
When a plant is fully grown, the player has an amount of time equal to the full growth time of the plant to pick the Berry; after this time, the plant will return to its sprouting stage. This regrowth can occur up to 9 times (for a total of 10 plantings) before the plant is permanently lost.
According to Bulbapedia, the time before a berry plant replants itself is equal to the amount of time it took to grow. Since the time it took to grow is different for each berry, the time before the "Berry Cycle" repeats is also different for each berry. Also, the cycle can only happen 9 times before it stops.
As for your Leppa berries, in Gen 3 a Leppa berry takes 16 Hours to grow, so you have 16 Hours to pick it before the cycle repeats. To find the growth rate for a different berry, look it up on Bulbapedia, they have a table with all the information you need on each berry's page.

Source: Bulbapedia
Hope I helped.
I felt this question needed a better answer, as the previous one was just a guess based on the mechanics of a different game.