Image via Wikipedia1. Statistically speaking, most religions that people have ever believed in have gone "extinct", just like most species that have ever existed on the earth are now extinct. Based on sheer probability alone, the chances of the Mormon religion surviving another 500 or 1000 years are pretty slim.
2. I think that all religions are in trouble of extinction due to advancements in science. To me, the push of science will continue to constrict the space that religion is able to exist in until most of the supernatural parts of religion are eliminated. It used to be that people accepted religion because they wanted answers: why do we have lighting? why do people do bad things? what happens when we die? Before science, the only source of the tough answers to questions like these was from religion. Now, we have already answered many of these questions, including the one about lighting. And, we're on the cusp of answering many more of these question.
A specific example of this that I'm reminded of comes from FMRI studies of the brain. The amount that this field has progressed in the last 10 years or so is astonishing, and it continues to advance every day. Among other things, scientist who study the brain using FMRI (among whom I have many colleagues) have been able to show quantitative differences in the brains of people with autism, depression, and schizophrenia. Remarkably, scientists have even been able to show differences in the brains of people with conditions once ascribed to "personal choice", like sexual promiscuity -- which calls into question how much conscious control people have over conditions like sexual addiction.
The point is that, as more and more of these questions -- particularly moral ones -- end up with scientific answers, religion is going to have a harder and harder time finding a niche, especially as this information is made increasingly accessible to the public and the public in general becomes better educated (especially in developing nations).
3. The Mormon church has the unique and undesirable position of having it's origins in recent history. While other religions, like the Protestants and general Christianity, have the cloak of time to protect them somewhat from scrutiny, most of the events of the Mormon origin story happened recently enough that written records were prevalent.
So, my guess is that Mormonism will one day cease to exist. It will be interesting to see if time proves me wrong or right.
