Given that your girlfriend was letting a property while she was abroad, the tax office will argue that she must have known that she should be completing tax returns to disclose the rental income, especially since she was already in the self-assessment system. They will also argue that she should have informed them of a change of address, even a foreign one. The fact that the reminders and penalty notices were not forwarded to her is not an excuse as far as HMRC is concerned I'm afraid.
Having said all that, your girlfriend can appeal against the tax return penalties and, if necessary, she can take her case all the way to an independent tribunal. You can read about the penalty regime here
and the appeals process here
. I'm afraid that there are few situations where the tax office will accept an excuse for the late submission of the returns and if they are still outstanding they should be completed and submitted as soon as possible. The second link I gave you sets out what HMRC consider to be acceptable and unacceptable excuses.
If I were your girlfriend, I would appeal by letter, albeit that the deadlines for appeals have probably been missed. If the first appeal is refused, then she should ask for a review of the decision and if the review upholds the first decision, then she should ask for the case to be taken to a tribunal. None of this should cost anything but time so as far as I'm concerned, there is really nothing to be lost. In addition, the tax office may think again if your girlfriend asks for a tribunal as there is no guarantee they will win at a tribunal.
I hope this helps but let me know if you have any further questions.