In 你把票放好, why is the complement 好 instead of 住?
Put your ticket away properly and don't lose it!


In order to interpret it properly, we should understand the English phrase "put away" correctly. I think this dictionary definition explains the sense of "put away" applied in this context well:


  If you put something away, you put it into the place where it is normally kept when it is not being used, for example, in a drawer.


In your context, "Put your ticket away properly" suggests that you should put your ticket in the place where you feel safe and comfortable to keep it. So, 放好 here makes more sense because it's indicating keep it properly. 拿住, however, denotes the sense holding it tightly preventing from dropping, which is a bit off from the context. 

P.S. 住 in 抓住 denotes the sense of sustainability. 抓住 and 抓紧 are often interchangeable in most of contexts.