Are there any 32-bit 3rd-party plugins present in the project?  My recollection of these kinds of symptoms steers my thinking to check if a plugin synth or effect is behaving badly (at least to check it out).
 
When this project is opened, do you see BitBridge running in Task Manager?
 
Also, is your Windows up to date on maintenance?
 
Do you have anti-virus software running?  Have you tried temporarily excluding Sonar paths or temporarily suspending the anti-virus software?
 
Are there any Windows Events showing critical errors viewable in the Windows Event Viewer?
 
Bob Bone
 

Quick update:

While I never figured out what caused this problem, I was able to open the project in 'safe mode'. When I enabled all of the plugins, as Paulo suggested, it seemed to work just fine. I simply re-saved the project with a different name and was able to continue working without any problems. Thanks for all the suggestions everyone!

Great news.
 
Now can you go back to your original post, edit it to add the word SOLVED in the title.