  Recently, several accreting M dwarf stars have been discovered with ages far
exceeding the typical protoplanetary disc lifetime. These `Peter Pan discs' can
be explained as primordial discs that evolve in a low-radiation environment.
The persistently low masses of the host stars raise the question whether
primordial discs can survive up to these ages around stars of higher mass. In
this work we explore the way in which different mass loss processes in
protoplanetary discs limit their maximum lifetimes, and how this depends on
host star mass. We find that stars with masses $\lesssim$ 0.6 M$_\odot$ can
retain primordial discs for $\sim$50 Myr. At stellar masses $\gtrsim$ 0.8
M$_\odot$, the maximum disc lifetime decreases strongly to below 50 Myr due to
relatively more efficient accretion and photoevaporation by the host star.
Lifetimes up to 15 Myr are still possible for all host star masses up to
$\sim$2 M$_\odot$. For host star masses between 0.6 and 0.8 M$_\odot$,
accretion ceases and an inner gap forms before 50 Myr in our models.
Observations suggest that such a configuration is rapidly dispersed. We
conclude that Peter Pan discs can only occur around M dwarf stars.
