I have a tenan just moved-in for over a month. Her dog kept breaking the wooden fence in the backyard and the neighbors complained to me. So I talked to her and she agreed that she would do something to prevent further damage. I sent her an email officially and asked her to response with a suggestion in one week.

Next day, she sent me an email and said her dog broke another piece again and she decided to get an electric collar to the dog. If it still failed, she would suggest another solution. I said okay and asked her to tell me the status after two weeks.

After over 3 weeks, she didn't send the update. I emailed her to give me the update, no response. Texted her again two days later, no response. 

I checked with the neighbors and he said no fence was broken since.

She has a tendency not to response my email, text and call. Except the time the AC had issue and she responded in one hour! 

In this case, should I continue chasing her for a response so I can close the case? Or let it go because no further damage?

it's getting difficult to deal with her when she ignores my communication. We have a scheduled AC tune-up later this month. I will send her a notice and mention if she doesn't response or not available, I will go open the door for the service. 

If sending all communications to her by mail, would that make a difference?