Basically on the trial date the expectation was that you STILL had to e-mail them to say today is your trial and that you understand it will be adjourned automatically. Seems like you didn't do it. So technically it's not entirely their fault - though, they should have told you to do so in that email.
That being said you can now prepare a set aside application (within 15 days of finding out that you've been convicted in absence) and fill out the Affidavit and submit it. Typically you will appear in front of a judge to explain and that judge decides whether the conviction can be set aside or not. But in your circumstances, I don't see how they can say no to setting it aside. Can just be chalked about to miscommunication etc. Also in this case they may just set it aside without you having to appear and explain etc based on the e-mails but I would do up the set aside application regardless and basically explain what transpired exactly in there.
Conviction will be set aside and then well keep the fight going.