I could not find any email log entries, so I tried to debug and found that there is no database table created after activating plugin.
SELECT COUNT(id) FROM abcde_email_log WHERE 1=1
Table 'database_com1.abcde_email_log' doesn't exist
SELECT * FROM abcde_email_log WHERE 1=1 ORDER BY sent_date DESC LIMIT 0, 20
Table 'database_com1.abcde_email_log' doesn't exist
Maybe related to this: http://wordpress.org/support/topic/plugin-email-log-cant-get-any-logs (as I know S2Member use wp_mail() and there are same symptoms - no logs, no error message).
Thank you for your help!