Mail keeps setting "Save drafts on the server" checked

Another good option that fixed the problem for me is as follows:

1. Quit Mail.app.
2. Log into Gmail in your favorite web browser.
3. Click on the gear menu and select Settings.
4. Click on the Labels tab.
5. Under System Labels, next to Drafts, click on show if unread and uncheck the Show in IMAP box. Now disable Store draft messages on the server.
6. Launch Mail.app.
7. Select Mail → Preferences…
8. Click on the Accounts button in the toolbar.
9. Click once on the account name and then click the Mailbox Behaviors tab.
10. Uncheck the Store draft messages on the server box.
11. Close the window and opt to save your changes when prompted.

^{Source: Apple Support Communities: Mavericks Mail app and Gmail Drafts folder}

Are you using Mavericks? This is probably related to the MANY Gmail related problems that have cropped up since it's release.

You are in luck though, as Apple has just released an update to solve many of said problems.

http://www.macrumors.com/2013/11/07/apple-releases-mail-update-for-mavericks-to-address-gmail-issues/