Do you have existing domain related email accounts? i.e.: you@yourdomain.com

You must have the email account(s) migrated away from us, or stored external to us, prior-to domain transfer out. You can share your current account access with your new registrar and they are allowed to migrate your email messages to their systems via IMAP access.

Any email message backup, printout, or migration must be complete before transfer is began. Just because you use a third-party email software on a computer, doesn’t necessarily mean that the messages are permanently saved there – as an example, if you use IMAP access in a third-party software, an email account erasure from our servers could cause your third-party software on your computer to wipe the data from your computer at next email sync attempt, depending on that software's configuration.
Once a domain is transferred away from us, the associated email account storages are permanently deleted from our servers. Webmail access to the account you had with us will no longer function, as the account will no longer exist.
Some third-party softwares do not work well, or at all, with having an old email account as well as a new email account - both with the same email address, setup in them.

Do you have FOR CERTAIN all the vital sent and received messages?

Other considerations:
-Do you have domain related email accounts setup into so many softwares/apps/devices – that the domain should remain with us, so that all the devices do not have to be re-setup? 
-Do your employees have the ability themselves, or do you have someone in your organization that can re-setup all the necessary devices with email, when provided the instructions from your new host?

As an alternative to transferring your domain away, we can point the domain at your website at your new host, while continuing to serve your domain and email for a monthly fee less than your current website package.
If you do decide to leave the domain and email hosted with us, WE MUST be given the dns settings for the new website at your new host. We are not responsible for any breakage of site DNS due to incorrect settings supplied to us for your new site host.

If we are to continue to provide email, we must control the domain on our registrar – there are many ways that a “blackhole” could happen, which we would be denied the ability to fix, if we tried to provide email on a now-to-be external-to-us domain.