There are several things that can cause me to lose interest in a story.
The first one that often causes me to quit on a story is when it stops feeling believable. All to often it seems that I find a story that has a great introduction, the characters are not only believable, but also easily related to, and it goes well, sometimes only for a few paragraphs, other times for chapters. Then something happens, normally to me its in the discussions between characters that makes it stop being real. Um, an example is like where instead of a 'real' conversation its fake, or unbelievable like when tommy talks to his friend ron and is like "ron, i know you like me, its ok, lets have sex".
I know thats a horrible example, but then again i'm trying to represent just that.
There are other things that can cause me to lose interest, but the lack of realism or believability is what does it to me the most. Comically, YSD, BM, DaBeagle, and several several others all have the amazing talent to not only bring the characters to life, but they make the stories believable and full of emotion. When a story has emotion and you can relate to or understand the characters, thats when you have a good story......if it has a good storyline, communication, and setting.
The loss of one of those, or the waining of excitement/details/activity in a story can definately make one lose interest.