RE: All of those scenarios do not seem to apply because the forms were working perfectly and stopped working without me doing anything at all.
Sorry but you almost certainly wrong. Your second comment matches the common symptoms seen in this forum on hundreds of occasions for a classic JavaScript Conflict.
See Contact Form 7 Email Issues - there is a link there that covers JavaScript Conflicts.
The plugin is working for me on WP 4.1 on many different websites and several different servers. Any issue you have is almost certainly due to something on your local WP install.
You will probably be mistaken if you focus on this happening since the last update - it's most likely just a coincidence.