Wondering if there's any research behind the most common password reset cycle I've seen of 90-days, and if there's any research that gives any insight into how to optimize password resets to reduce password reuse.
The research shows that requiring time-based password changes increases re-use (users will use a password from another site, since they've already got it memorized, or will use a near-duplicate of their previous password), decreases password complexity, and increases the odds of the password getting written down somewhere.
In short, if you want to minimize password re-use, don't require time-based password changes. The best way I've seen to encourage unique passwords is to provide the user with a randomly-generated password at account creation, rather than letting them specify a password.
I assume by "frequency of password resets" you mean password aging, that is "user must change password after X amount of time".
By itself, password aging has no impact whatsoever on password reuse. By definition, password aging simply says the user must choose a new password after a certain amount of time. The key parameters that cooperate with password aging to prevent password reuse are "password history" (how many previous passwords the system must keep track of for each account) and "minimum password age" (how long a user must wait after changing a password before they can change it again.
Say your system requires users to change their password every 180 days, has a password history of 6, but has no minimum password age.
This means if a user only changes passwords when the system requires him/her to, they can reuse their first password after 2.5 years (or 3 years, depends on how you count it.)
Without a minimum password age, a user could change his password, and then change it again 6 more times right away, and eventually go back to his first password.
A minimum password age policy makes this much harder. A minimum age of 24 hours means it takes a week to go through all those iterations and get back to the original password. Make the minimum age 7 days and now you are in the 1-2 month range.