You can present a cheque at a bank for any number of times during the period of its validity [in your case three months from 20th June, 2013]. But once you send the mandatory legal demand notice for payment of money within one month of return of cheque for insufficiency/ stop payment instruction, the cause of action arises immediately on the expiry of 15 days from the date of receipt of notice by the drawer and the money remaining unpaid. Cause of action arises only once and this is the necessary restrictive meaning given under Clause (b) to Section 142 of N.I. Act.
Therefore, if you have not sent a legal notice to the drawer as yet, don't worry, you can still present the cheque at your bank even after lapse of 01 month of return of the same for insufficiency/ stop payment instruction and legal notice having not yet been served . If again it's returned for the same reason, then also you can send the mandatory legal demand notice for payment of money.
Remember to file the complaint u/s.138 N. I. Act within one month from the cause of action. [note: Cause of action= failure to make payment within 15 days from date of receipt of the legal notice by the drawer]