I have an Aprilaire that is the powered model. The humidstat goes on
the cold air return plenum. There is also a temp sensor that goes
outside. It's function is to reduce the humidity as the temp decreases
outside. From the behavior sited, it sounds like the humidistat is
bad. If it's set just short of the point where it would turn on, then
with the heating system running regularly, it should come on before too
long. Sounds like its broken and you essentially have just an on/off
switch.