I am going to assume when you say the "Persist Cohort option" you are referring to the "Rolling Calculation"??
Here is the basic setup options of a Cohort Table:

You choose your Inclusion Criteria, and your Return Criteria (I am doing a simple "Visit" cohort here).
My Granularity is "Month" so if I were to look at the last 6 months, then for the fill 6 Months, Visitors who came to my site in May would be included, then if they visited in June they would show in that column, etc...
If they did not visit my site in July, this is where the Rolling Calculation makes the difference...
If I don't use Rolling Calculation, the user is not included in July, but if they come back in August they will appear in the August column...
If I am using Rolling Calculation, then the visitor must maintain retention in each month to stay included.. so if they didn't visit in July, but came back in Aug, they still won't be included... Only visitors who come every month will make it to the end of the cohort, everyone else will lose the retention.
Example:
|
Visited Site |
Not Using Rolling |
Using Rolling |
Month 1 (inclusion) |
yes |
1 |
1 |
Month 2 |
yes |
1 |
1 |
Month 3 |
no |
0 |
0 |
Month 4 |
yes |
1 |
0 |
Month 5 |
no |
0 |
0 |
Month 6 |
yes |
1 |
0 |
Cohorts are designed to look at visitors over multiple visits, leaving the site is expected... it really depends on what your inclusion and return criteria are set for, as well as if you are using Rolling Calculation that will determine if the visitor is included in the cohort.