I thought I had responded to your query yesterday, but I don't see my response here. Maybe it got lost in the forum design transition.
I enumerated several possible reasons for what you are seeing and asked some questions that might help somebody to help you. I'll try to recreate some of the questions.
If you have multiple email accounts, are you having the problem on all of them that you had before 2012 or only some of them?
What type(s) of account is/are involved (POP, IMAP, other)?
Was your pre-2012 email stored on your provider's servers or in "On My Mac" folders?
If on your provider's servers, does your provider have a stated retention limit?
If in "On My Mac" folders, are you still using the same Mac? If not, did you migrate email folders?
Did you change computers, disks, email providers, or the like around the end of 2011?
You didn't answer the question about where your pre-2012 mail should have been stored (on provider servers or "On My Mac" folders) or the one about migrating email when you changed computers.
If you use the Gmail web interface, can you find the messages you seek?
Same question for Yahoo
If 1&1 has a web interface, same question.
I am not sure if the pre- 2012 mail folders are stored on the "on my mac" folder, not sure how to look for this?
The email I tried to trace was written on 1&1 and for some strange reason its not web interface, spoke to their customer support team and it will take 4 days to try and retrieve it.
thanks for your help.
I hope that 1&1 support can find your message for you.
As for telling whether any of your other messages might have been left behind on your old Mac Pro, you would to look on that computer if you still have it or in a backup of that computer if you took one. Were you in the habit of filing email in dated or themed folders that you no longer locate?