How to get an advisor to finish their part of a publication when they have not done anything on it for over a year? I graduated from a reputed North American university with a master's degree in 2013. Due to severe personal problems (deaths/illness in the family, war-torn homeland, divorce, financial issues, and so on), it would be fair to say that I did not perform well. My thesis had a critical error which was duly pointed out during my defense by my examiner. My advisor had not noticed it before. I managed to pass but with major corrections to the thesis. 

While I was waiting for the situation in my home country to settle down, we improved the results significantly. We wrote much of a paper with the agreement that we would correspond over email when I go back home to finish it and send it for publication. 

This was a year and a half ago. I am back home and I have been trying to get her to finish writing her part but to no avail. Once every couple of months she responds with "I need more time" but that's about it. It would be a huge help in my career to have a paper published. But I am paranoid about being rude to her and keep nagging her because I need her reference if and when I decide to apply for a PhD later. Also I believe she's a genuinely a nice person! So my questions are, 


Is a year and a half a normal amount of time to write on a paper in
which the research is finished? 
How do I politely convince her to hurry up?
Is a year and a half a normal amount of time to write on a paper in which the research is finished? 


No, this paper should've been finished a year ago. 

The research is done, so you are not waiting for something else to fall into place for your paper. You already tried writing your former advisor's portion of the manuscript to no avail. Your former advisor did not even catch a critical flaw in your thesis. I hate to say it, but it sounds like your former advisor is quite a bozo.


  How do I politely convince her to hurry up?


If you've not already done so, send your former advisor your "final" draft of the manuscript (including the parts you wrote for her). Give her a timeline for returning suggestions/modifications to you. If that doesn't work, you might have to get on the phone and talk to her about how important it is for you to submit this paper. If this fails, you may need to move on, and hope that at some point in the next year or two that she finally matures enough to help you out.