Is there any way to disable OR password protect my iPhone to prevent someone from turning it off? If my phone is stolen, I would think the first thing a thief would do is turn it off.  Is there any way to disable or password protect this via settings (which I doubt) OR a cydia tweak?
If you've jailbroken your phone, try either iGotYa or iCaughtYou Pro. They offer the best protection against theft without using a commercial MDM system, in my opinion.

PowerGuard will provide the power feature you want, but it won't protect the phone from being placed in DFU mode. Still, a combination of both PowerGuard and one of the above apps is better than nothing.







This won't prevent powering it off, but, if you've upgraded to iOS7:


  With Find My iPhone turned on in iOS 7, your Apple ID and password will be always be required before anyone can:
  
  
  Turn off Find My iPhone on your device.
  Erase your device.
  Reactivate and use your device.
  
  
  There is nothing you need to do except to keep Find My iPhone turned on and remember
  your Apple ID and password.


From a device security perspective, I think this would accomplish the same thing by rendering your device useless to anyone who steals or finds it.