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?
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