I would say you are doing the right things here. I would hold onto the money and keep trying the mail, etc. I would be careful about going to the house, but maybe leave a note, etc. If you don't reach the former tenant in another month or two deposit the funds in an escrow account. If you know anyone else who knows her or you know her email address, etc. try those as well. Just document, document, document everything. These funds are not yours so be absolutely sure to keep them separate. This is obviously mostly common sense type advice but its unusual for someone to NOT want money due them.
This is not legal advice nor intended to create an attorney-client relationship.
I think you have acted more than reasonably in terms of attempting to return the deposit. However, if your former tenant is not interested in this money, placing it in a separate bank account seems to be the only available option.
The response given is not intended to create, nor does it create an ongoing duty to respond to questions. The response does not form an attorney-client relationship, nor is it intended to be anything other than the educated opinion of the author. It should not be relied upon as legal advice. The response given is based upon the limited facts provided by the person asking the question. To the extent additional or different facts exist, the response might possibly change.
The biggest thing to be worried about is that the tenant could pop up at any time and ask for the deposit. A separate savings account with a modest interest rate would be the most reasonable place to keep the money. You could send a letter by certified mail to both addresses as well to demonstrate that you've made a reasonable attempt (I agree that you already have made a reasonable attempt, but this would help you prove it).
This is general information only and is not legal advice, nor has an attorney-client relationship been initiated. I am only a licensed attorney in Pennsylvania.