When I happened to notice, courier-mta was spewing out a lot of errors. In fact, it was receiving mail, but apparently it wasn’t able to send any. The error was:

Address family not supported by protocol

Hmm, I thought it might be something related to IPv6, but it turned out that /etc/resolv.conf simply wasn’t written correctly. Specifically,

nameserver 127.0.0.1

Even though it had to be specified like that, for some crazy reason I had written localhost instead. orz