Turn off encrypted backup on iPhone that has a profile without removing profiles

Solution 1:

When you have a profile that enforces encryption of backups, you really only have three options:

1. Live with the encrypted backups and do nothing.
2. Get someone to remove the profile (or wipe the device along with the profile and start over being careful to not allow profiles that force you into encrypted backups).
3. Somehow exploit a bug or flaw in the security of iOS and bypass this lock. I would expect you to pay big money or have some assistance from NSA-like organization to accomplish this last item unless someone publishes a weakness in iOS that we could take advantage of to bypass the security your iPhone has configured.

As it stands, you will likely have to remove the profile to bypass the restriction that iOS has on not doing a backup in the manner you wish.

Solution 2:

You can't access your old encrypted iPhone backups if you can't remember the password. However, iTunes can create a new backup of the iPhone without encrypting the backup, see here for details. http://support.apple.com/kb/ht4946

Alternatively, you could use a 3rd party app to backup your iPhone without iTunes.