If you are not receiving email sent to you via a contact form on your site, the chances are that you are using a third party email solution, and your server is trying to deliver the mail locally. To rectify this, you just need to disable mail on the domain via Plesk or cPanel. 

Disabling local mail via Plesk

1. Login to your Plesk control panel.

2. Click on Subscriptions then the name of the domain. 

Plesk Subscription

3. Click on the 'Mail' tab. 

Plesk Subscription Mail Tab

4. Click on 'Change Settings' then untick the 'Activate Mail Service on This Domain'.

Disable Mail

Disabling Local Mail Using cPanel
1. Login in to WHM. Click on Account Information -> List Accounts.

2. Log into the domain's cPanel by clicking the 'cP' icon.

3. Click MX Entry from the Mail section. Now choose Remote Mail Exchanger in the Email Routing section.