missing emails imap mac mail

I'm looking for emails that I sent my accountant January/february this year and they are gone! Can't see them in time machine either... can one search email in time machine? It doesn't seem so for me.

imac/iphone/macbook

-I'm looking specifically in my sent folder, but expanded search to All also

-I transitioned from pop to imap a few months ago when I started using the macbook and wanted more sync across computers.

-it's not like all the messages are gone... there are plenty of emails but the specific ones I'm looking for are not there now, not sure how many others might be gone

-I checked all my computers and none are set to pop none for erase off server

-I did have trouble setting up mail on my macbook... so I switched to thunderbird for that computer

What is the procedure for seeing emails on time machine? Don't I start it while in mail program and just roll the time back and I should see archived versions??

-The other variable is I upgraded from snow leop to mt lion about this same time- Jan/Feb so I could use the cloud. But wouldn't my old leopard mail archives still be intact even if lion did some mail restructure??

thanks

Bob