Really an AP should not reboot no matter what you send through it, of course. I have been working with enterprise WLANs for many years and have never seen that.
Just for curiosity, I would hookup a PC with WireShark and connect via Ethernet hub between AP and LAN; then create a trace doing Gpupdate via wired and compare with WLAN gpupdate. I would guess there is something like a flood of malformed packets or some unreasonable number of authentication requests that are killing the AP. The AP is a mac-layer bridge, so it is logically no different than an ethernet cable, from a connectivity perspective.