The IRS e-file processing system generally accepts or rejects tax returns within seconds or minutes; therefore, if your return is accepted, and you later discover that you made an error on your first electronically filed return or you have received additional information (i.e. a Form W-2 Wage and Tax Statement) that needs to be included in the return, you will need to file an amended return. You should NOT re-submit a second return as it will be rejected with the "Previously Accepted Return" message.
The appropriate way to handle errors made on an electronically filed return or additional information needing to be included in the return is to file an amended return. If you determine an amendment is necessary, see the Form 1040-X - How to Create an Amended Return FAQ.
Note that any link in the information above is updated each year automatically and will take you to the most recent version of the document at the time it is accessed.