If you're using One-Time Offers (WordPress Dashboard s2Member General Options One-Time-Offers (Upon Login)) to show members a special page upon their first login, you may want to reset the login counter if you plan to show those One-Time Offers to members after they upgrade their membership.

The number of logins is not reset when someone upgrades from one level to another, so a member who upgrades from one level to another would not see a one-time login offer that is configured to be shown upon the first login.

However, you could reset the login counter to 0 whenever a user is upgraded from one level to another. To do this, create an MU-Plugin with the following code, which will trigger whenever a user's role is changed (e.g., when they are upgraded from one Level to another).

Create the following directory and file: wp-content/mu-plugins/s2-reset-login-counter.php

add_action('set_user_role', function($user_id, $new_role, $old_role)
    if(strpos($new_role, 's2member_') === 0 || $new_role === 'subscriber')
        update_user_option($user_id, 's2member_login_counter', 0);
}, 10, 3);