I've seen many series that just get discontinued, even popular ones. I'm talking about manga and light novel adaptations. Even though a lot of the story still remains left, and the first season gets critical acclaim. Some examples are Kaichō wa Maid-sama! and Baka and Test. Why do so many series stop after season one?
There are tons of reasons for animes to be discontinued. One of the most common ones would be lack of sales. A anime might become pretty popular, and watched a lot. But if the sales do not match, no second season will be made nonetheless due to money issues.
Popularity ALSO plays a factor. If the first season is not popular enough towards viewers than a second season is just a waste of cash. However, there are SOME anime titles out there who produced a second season countless years after the first season; so hope is not all lost for fans who wishes for a second season (e.g. Inuyasha finished airing in 2004, however it's sequel series Inuyasha: Final Act started in 2009-2010, completing the entire series since the manga ended in 2008).
The loss of sponsors is not uncommon which can lead to huge budget cuts, which sometimes lead to debt which first has to be covered for.
Keep in mind that studios use the Japanese sales numbers as reference point for sales, which differ quite a lot from European/American sales
Yes, I'd assume the reason for this is because anime is naturally common in Japan. In the US it's something different, something maybe a little rare, so people can see it as a targeted interest. If you were in Japan and said "I'm a big fan of anime" people would probably not notice, just as if a Japanese person said "I'm a fan of American sitcoms" because it would be such a wide genre that most everyone would find something that they like. Both people would probably end up getting a response like "oh... that's nice.... which ones?" etc.
Sometimes it might also just be a issue between the director and the mangaka.
Fruits Baskets case it was originally going to be longer, but the creator of the manga didn't like the director or something (lol I can't remember exactly) and she didn't allow them to continue the anime.
Some other reasons although less common then money issues would be
- No free time slot for broadcasting
- Lack of material (but you're talking about ones with story left to tell so count this one out partially)
- Lack of studios that want to take the job (happens more often then you think)
Most anime series are produced to promote the source material (manga, light novel, etc.). Thus for the producers its more important if the sales of the source material were boosted by the anime adaption. So even if an anime is quite popular - it should be noted that even quite successful anime only sell between 3000 and less then 10000 (more than that is rare is considered a very successful anime) discs per volume - there is often no point in producing another season if the sales of the source material increased sufficiently.