This answer stated that hitting the Apple II Reset key twice, in quick succession, could cause DOS to be disconnected from the I/O hooks. I don't understand why that would happen.
Quick background: the reset handler in the original monitor ROM would reset the character I/O hooks and video mode, then drop the system into the monitor command-line. The "autostart" ROM added a feature where a vector could be placed at $03F2 that would get control after the monitor finished its part. When DOS was booted, it put its warm restart vector ($9DBF) there, so that it could reset the I/O hooks to point to itself after a reset. (It does some other stuff too; hooks are set at $a851.)
My expectation would be that hitting reset a second time while the first was active would simply restart the process, and lead to the same state. I don't understand why the second reset would break things.
According to the comments in the published source, the "beep" noise emitted by the monitor reset handler is partly there to mitigate effects from key bounces:
fa82: 20 3a ff jsr BELL ;causes delay if key bounces
(The beep was present in all versions of the ROM.)