I use Microsoft Outlook as my email client but I also have separate Gmail account on my iPhone 4S which has no problems sending or receiving emails. On my Outlook account at home I can always receive and send emails but only receive from my iPhone. When sending a message from my iPhone it says that the recipient has been rejected by the server. It keeps trying to send but keeps rejecting.
There are two methods for adding an Outlook account to your iPhone:
In the Mail, Contacts, Calendars --> Add account section of the Settings app:
When adding the account you select "Hotmail" (Outlook) and type in your email and password.
You select "Other" and type all information required.
Unless its too hard and it may delete something that you need, delete the mail account, and create another one using the opposite method of how you originally created it.
This may help. (If it does, upvote or confirm)
When you add an account to your email accounts, have you entered the correct information?
I have my work email address connected through MS Exchange fine, and is on my iPad.
Email: firstname.lastname@example.org Server: mail.outlook.com Domain: outlook.com Username: email@example.com Password: ***** Description: Outlook Emails Use SSL: On
Obviously, you replace the details with your own.