I think this is wrong:

while (<$sock>) {

Looking at perldoc IO::Socket, you need one or two things:

• set IO::Socket::timeout to some reasonable value, maybe 1 minute, so you don't wait forever.
• Test IO::Socket::connected after reading from the socket.

TCP has a teardown sequence: the sender closes its port; the receiver acknowledges the close and closes its own. . It's very unlikely that rebooting the PBX interferes with that. Your TCP stack knows the sender is gone, but because you're not timing out, you never learn of it.