This is what I beleive that Ursa is still alive
1. That she killed Azulon because when Azula told her what he said to Ozia she got mad so that night she went in his room, and some how she killed him. Then with out thinking she desited that she should leave worried that some how they might find out she did it. But before she left she had to say good bye to Zuko, just she had to make it quck before someone saw Azulon's dead body, and her leaving they might make a conection that she did it. She said to Zuko: Everything I've done, I've done to protect you. Remember this Zuko. No matter how things may seem to change, never forget who you are. She said that so he will not think different about her if he found out she killed Azulon. Ursa was waring a something that has a hood on it so people will not know it was her, so can exscape with ou anyone seeing her. That is something I will wair if I was trying to run away.
2. When Zuko was sick on the epi "The Earth King" he saw his mother and she said Zuko help me. That could mean that she is alive because why would the creaters make that scene if she was not even alive. There has to be some conection to that, and to his mom's dissaperence.
I just hope they put her in book 3 and for her to tell everyone were she was at. Maybe she will meet up with Aang and the gang but they will not know how she is. Then they will come up aganst Zuko, and she will show up, and say something like Zuko please don't fight the Avatar, and it will be this big touching reunion for Zuko and his mom even maybe for Azula also. If not that then I just hope Zuko tries to go and find her sometime in book 3. I just can't wait to find out.