Starting with 4.3BSD and System V Release 3, signal handlers remain installed after a signal occurs. So, yes, the requirement to re-install a signal handler is some super ancient (many decades ago) stuff. No modern system and no POSIX compliant system will cause an installed signal handler to be affected. I would think that the Perl docs should be updated.
Now, this while() loop in the reaper is definitely needed! Signals are not "queued" for delivery. When a signal occurs, always interpret that to mean "at least one and maybe more than one of this signal has occurred".
Update: Wiki ATT releases SVR3, SVR4. SVR3 was GA'ed in 1986. I figure after 25 years, we don't have to worry much about R2 any more!