Update: As of 30/07/2020, the part of this Article which refers to non-live Sites may need updating. You can continue to follow the advice for Live Sites.
The most likely reason for this is that the majority of Email providers will block emails that claim to be sent from one domain, but are actually sent from another. You can learn more about DMARC policies here.
When you set up Workflow and Autoresponder Emails, there's a field called "From" which is used to define the address sending the email.
Recipients of the Workflow and Autoresponder Emails will see this as the email address the message was sent from. However, while you're testing your site the email is actually sent from your development domain.
Example on a live site:
From Address - firstname.lastname@example.org
Actual domain the email is sent from: agencydomain.staging.london.platform-os.com
Spammers love to pretend to be from legitimate sites e.g. a bank or your Client's website. So the DMARC policy on a domain helps protect their brand and customers. If an email is sent from an unknown domain pretending to be authorised to use that email address it is blocked. This is great from the internet and great for you Client, but not great for testing.
The Solution (for non-live sites)
The best solution is to send from an email address belonging to the domain you're sending from. This doesn't need to be a real email address, the important thing is that it's not pretending to be from a domain it's not really from.
You'd replace the domain in the example with the development domain you're using on the Site you are building.
The Solution (for live sites)
Your Client will have a real "from" address they'd like you to use. It's important to remember to switch to this before the Site goes live.
This address will likely be based on the same domain as the Site - and you should have no issues.
If you do have issues, you'll need to contact the person who administers the email service, and make sure its DMARC policy whitelists the domain the emails are sending from.