I just installed this plugin and tested it completely. It works. But for some reason my contact form /still/ won't send out email, and yes, I checked spam folder.
I use AWS offload but my server host also updated the php version recently. It also could be the base theme's built-in contact form scripting, I suppose, but I kinda assumed your plugin would override that without me having to get into the parent theme and rewrite a bunch of stuff.
The form is at http://www.kristinachilds.com/contact/ and can be easily re-enabled by uisng dev tools to remove the disable_form class from the container div. I'm not sure if that will tell you anything you need to know, but it's worth a shot.
Follow-up question: is there any way to learn exactly how many new client inquiries I've missed? The only reason I even knew this stopped working is because someone followed up with me using the olark chat box after not getting a response from me via the contact form. If there is a log somewhere I could get my hands on, I would be a super happy lady!