  We carry out a set of self-consistent N-body calculations to compare the
decay rates of satellite dwarf galaxies orbiting a disc galaxy embedded in a
dark matter halo (DMH). We consider both spherical and oblate axisymmetric DMHs
of aspect ratio q_h=0.6. The satellites are given different initial orbital
inclinations, orbital periods and mass. The live flattened DMHs with embedded
discs and bulges are set-up using a new fast algorithm, MaGalie (Boily, Kroupa
and Pe\~{n}arrubia 2001).
  We find that the range of survival times of satellites within a flattened DMH
becomes of the order of 100% larger than the same satellites within a spherical
DMH. In the oblate DMH, satellites on polar orbits have the longest survival
time, whereas satellites on coplanar prograde orbits are destroyed most
rapidly. The orbital plane of a satellite tilts as a result of anisotropic
dynamical friction, causing the satellite's orbit to align with the plane of
symmetry of the DMH. Polar orbits are not subjected to alignment. Therefore the
decay of a satellites in an axisymmetric DMH may provide a natural explanation
for the observed lack of satellites within (0-30) degrees of their host
galaxy's disc (Holmberg 1969; Zaritsky and Gonz\'alez 1999).
  The computations furthermore indicate that the evolution of the orbital
eccentricity $e$ is highly dependent of its initial value e(t=0) and the DMH's
shape. We also discuss some implications of flattened DMHs for satellite debris
streams.
