How can highly virulent but uncommon diseases (like ebola) maintain a stable equilibrium?
Viruses and other disease causing organisms are usually in an ecological steady state in different organism, called a vector.  When they start to infect another organism similar enough that they can reproduce, they may turn out to be more virulent or fatal than is optimal for the organism.

The classic example is the case of influenza outbreaks, the flu virus is causing mild infections in other animals such as birds or pigs and then a human being catches it and it may be serious or even fatal.  This is classically because the viruses lytic cycle (where it reproduces and then kills host cells) is not tuned to the equilibrium ideal for viruses in the new human environment, which is not fatal which gives the virus the best chance of reproduction and retransmission.   

In the case of Ebola and Marburg viruses the vector is not known but there is speculation and research going on. So in the extremely rare handful of events where these hemorrhagic fevers have been caught by people they fatal.  

Its the non-equilibrium case where the virus is not adjusted to human hosts and adjusted for its vector population where it is usually most dangerous. 

If these viruses were allowed to persist they would theoretically come to the point where it wasn't fatal.  The problem being that people would die and there is always the risk that the virus would burn through all possible human hosts before it adjusts... 

I want to say that this is all driven by evolutionary forces.  If the environment encourages pathogenic characteristics then human pathogens can persist forever.  Flesh eating bacteria and MRSA and other antibiotic resistant bacteria have found a competitive environment where causing disease and death are the only way to go - hospitals with antibiotics. In the case of Ebola/Marburg, there may be a disease reservoir of monkeys acting as a pool for the high fatality strain.  Anything can happen with the right geography and dynamics. 

If you've been thinking to yourself, 'what are the odds that a virus or bacterium would be extra virulent versus not infectious at all?', you are right. One should also note that fatal outbreaks are rare and exceptional.  There are clearly plenty of cases where viruses or pathogens from other organisms can't get any traction at all in humans.  We are practically swimming in viruses and bacteria all the time.