  WISEA J080822.18-644357.3, an M star in the Carina association, exhibits
extreme infrared excess and accretion activity at an age greater than the
expected accretion disk lifetime. We consider J0808 as the prototypical example
of a class of M star accretion disks at ages $\gtrsim 20$ Myr, which we call
``Peter Pan'' disks, since they apparently refuse to grow up. We present four
new Peter Pan disk candidates identified via the Disk Detective citizen science
project, coupled with \textit{Gaia} astrometry. We find that WISEA
J044634.16-262756.1 and WISEA J094900.65-713803.1 both exhibit significant
infrared excess after accounting for nearby stars within the 2MASS beams. The
J0446 system has $>95\%$ likelihood of Columba membership. The J0949 system
shows $>95\%$ likelihood of Carina membership. We present new GMOS optical
spectra of all four objects, showing possible accretion signatures on all four
stars. We present ground-based and \textit{TESS} lightcurves of J0808 and 2MASS
J0501-4337, including a large flare and aperiodic dipping activity on J0808,
and strong periodicity on J0501. We find Pa$\beta$ and Br$\gamma$ emission
indicating ongoing accretion in near-IR spectroscopy of J0808. Using observed
characteristics of these systems, we discuss mechanisms that lead to accretion
disks at ages $\gtrsim20$ Myr, and find that these objects most plausibly
represent long-lived CO-poor primordial disks, or ``hybrid'' disks, exhibiting
both debris- and primordial-disk features. The question remains: why have
gas-rich disks persisted so long around these particular stars?
