RHEL6 serial console does not accept input when switching to runlevel S from a higher runlevel

Issue

When switching into runlevel S, the sulogin command does not accept input over the serial console. Entering any characters causes sulogin to say "Login incorrect" and reprint the login prompt:

Give root password for maintenance
(or type Control-D to continue): 
Login incorrect.
Give root password for maintenance
(or type Control-D to continue): 
Login incorrect.

When returning to runlevel 3, there is no login prompt available on the serial console.