  The evolution of protostellar outflows is investigated under different mass
accretion rates in the range $\sim10^{-5}-10^{-2} {\rm M}_\odot$ yr$^{-1}$ with
three-dimensional magnetohydrodynamic simulations. A powerful outflow always
appears in strongly magnetized clouds with $B_0 \gtrsim B_{\rm 0, cr}$
$=10^{-4} (M_{\rm cl}/100 {\rm M}_\odot){\rm G}$, where $M_{\rm cl}$ is the
cloud mass. When a cloud has a weaker magnetic field, the outflow does not
evolve promptly with a high mass accretion rate. In some cases with moderate
magnetic fields $B_0$ slightly smaller than $B_{\rm 0,cr}$, the outflow growth
is suppressed or delayed until the infalling envelope dissipates and the ram
pressure around the protostellar system is significantly reduced. In such an
environment, the outflow begins to grow and reaches a large distance only
during the late accretion phase. On the other hand, the protostellar outflow
fails to evolve and is finally collapsed by the strong ram pressure when a
massive $(\gtrsim 100 {\rm M}_\odot)$ initial cloud is weakly magnetized with
$B_0 \lesssim 100 \mu {\rm G}$. The failed outflow creates a toroidal structure
that is supported by magnetic pressure and encloses the protostar and disk
system. Our results indicate that high-mass stars form only in strongly
magnetized clouds, if all high-mass protostars possess a clear outflow. If we
would observe either very weak or no outflow around evolved protostars, it
means that strong magnetic fields are not necessarily required for high-mass
star formation. In any case, we can constrain the high-mass star formation
process from observations of outflows.
