Why is untreated trypanosomiasis invariably fatal in humans?
African trypanosomiasis, or sleeping sickness, is caused by the protozoan Trypanosoma brucei, a single-celled eukaryote.  Being eukaryotic, it has a cell nucleus and a larger genome than most bacteria; it also has a flagellum with which it can propel itself.  Infection with T. brucei occurs via the bite of a blood-sucking fly, one of several species of tsetse fly.

The mammalian immune system has a difficult time with T. brucei because of an effective set of adaptations.  The protozoan's surface maintains a dense coat of a particular glycoprotein on its surface which generally hide other necessary surface features such as chemical receptors and ion channels. Since it is this glycoprotein that the adaptive immune system will encounter, that molecule is the one which it will develop antibodies to recognize.  

Within a few days the protozoans would be recognized and soon eliminated by the immune system except that T. brucei at random times changes the glycoprotein used as its surface coat.  The mechanism that does this is called a variant surface glycoprotein (VSG) expression system.  The organism has a repertoire of about 1500 different proteins to  select from to use for a new glycoprotein coat.  The overall effect is that by the time the immune system is able to flood the body with the antibody type it has developed, most of the T. brucei population is not recognizable by those antibodies. T. brucei devotes a significant portion of its genome and its protein production to this immune evasion system.