Step 1: Launch the Settings app
Step 2: Choose Mail Contacts and Calendars
Step 3: Select the account with which you are having trouble syncing the Sent folder
Step 4: Under IMAP tap on your Account. (NOTE: If it says POP, then you have to delete the account and re-add it as an IMAP account).
Step 5: Choose Advanced at the bottom
Step 6: Under Mailbox Behaviours, tap on “Sent Mailbox”
Step 7: Ensure that the folder called “Sent” is checked off under the “On the Server” section