What is the status of the message? When a message is in quarantine or queued for retry then you should be able to see it, otherise the message is not stored on the system. The same applies for downloading the message.
I believe you just can see messages, which the MEG has not delivered in any case.
So fare, I don't saw an option, where you can store already delivered messages for a longer time at the appliance.
The only option I know is "Audit Copies" (Email | Email Policies | Policy Options | Notifications and routing | Audit Copies), where you can send a copy of any e-mail to a different e-mail address for troubleshooting.
From the manual (p61 of the 7.6 admin guide):
There may be other queued message viewing options, but if the message is delivered or dropped, the only option would be to turn on Dump input/output email to disk (Protocol Configuration --> Protcol Settings (SMTP)). This is generally not advised unless you are troubleshooting issues with the MEG malforming messages, as it will cause a performance hit (probably small), but definitely fill the disk in a hurry.
Is this setting availible at the 7.6 olny. At the 7.5.2 I can't see a Dump option in this section.
Dumping so much data to the appliance is truly an option only when support need this, not for permanent production use.