I had the same problem with only receiving emails when checking the HTML email box.
My problem was not having <p> tags. I see you do however. I wonder if the form fields you have in there are making it not work?
When mine wasnt working, this is how mine looked:
Thank you for your interest in COMPANY NAME! We will get back to you shortly.
—
This e-mail was sent from a contact form at COMPANY NAME
(https://www.COMPANYNAME.com)
<img src=”https://www.COMPANYNAME.com/wp-content/uploads/2015/09/logo_sm.jpg”/img>
Then I added <p> tags and it started working:
<p>Thank you for your interest in COMPANY NAME! We will get back to you shortly. </p>
<p>–
This e-mail was sent from a contact form at COMPANY NAME
(https://www.COMPANYNAME.com)</p>
<img src=”https://www.COMPANYNAME.com/wp-content/uploads/2015/09/logo_sm.jpg”/img>
I’m going to try adding the form field info as well
** UPDATE**
I added the form fields and it works perfectly for me.
<p>Thank you for your interest in COMPANY NAME! We will get back to you shortly. </p>
<p>–
<p>From: [name]</p>
<p>Company Name: [company-name]</p>
<p>Customer Name: [name]</p>
<p>Phone Number: [phone-number]</p>
<p>Email Address: [email-address]</p>
<p>Company Address: [company-address]</p>
<p>Additional Info/ Questions: [info-questions]</p>
<p>–
This e-mail was sent from a contact form at COMPANY NAME
(https://www.COMPANYNAME.com)</p>
<img src=”https://www.COMPANYNAME.com/wp-content/uploads/2015/09/logo_sm.jpg”/img>