Oscillators with different configurations
So why does this happen? Why is it that the "configuration" on the
  first circuit works out fine as opposed to that of the second circuit?


Because the Colpitts oscillator is idealized and you won't get any bias current through the capacitors for the transistor to work with. Capacitors block DC and hence bias currents are blocked. Try a non-idealized Colpitts oscillator instead (see below for one type of Colpitts oscillator). The Hartley has inductors that readily pass DC bias currents.



Picture from here.