That depends on what your favorite show is. Most sitcoms go off the air in 10 years or less. But Jeopardy has been on the air for four decades. MotorWeek has been on the air since 1981. Wheel Of Fortune has been on the air since 1975, and so has Saturday Night Live. NOVA has been on the air since 1974. Sesame Street has been on the air since 1969.
And if your favorite program is a national news program, I don't see national news programs on broadcast TV disappearing unless broadcast TV itself disappears.