There is no limit on how long you can study. I studied from the time I was about 10 and I finally got baptized when I was 17. it depends on the person who is studying and the progress they are making. Yes a study can be terminiated if it is determined that the person is not making progress or it is just a pointless study.
Example being I knew someone who was studying with a Mormon and the Mormon just refused to acknowledge that the Trinity didn't exist and that God and Jesus were 2 seperate people. The study was terminated shortly after that. In the case of an Elder outside of the study deciding that it would be best to terminate that study, I'm sure it was discussed and came to the agreement that it wasn't progressing and wasn't appropriate to continue the study.