Is it specifically a problem with Star Trek, or is American TV generally just more of a difficult climate for Sci-Fi shows these days?
For example, if Doctor Who was an American show, would that likely have been cancelled by now?
A lot of it has to do with money--sci-fi shows (especially space-oriented ones) have always been very expensive and difficult to produce in Hollywood since day one, and shows that don't have a big enough audience to justify their expense get cancelled fairly quickly (regardless of how loyal a cult following they may have). The same can be said for any TV show in any part of the world, really.
These days, a viewership between 12-15 million is ideal for a major US network, but smaller outlets can get away with less--but the shows they have tend to operate with smaller budgets as well.