The problem occurred again, and these messages showed up in the log-
01/08/2014 11:29:18.000 kernel[0]: process Google Chrome He[1009] caught causing excessive wakeups. EXC_RESOURCE supressed due to audio playback
01/08/2014 11:30:50.103 SophosWebIntelligence[63]: tcp_connection_destination_setup_socket_events 2477 kqueue() failed 24 - Too many open files
01/08/2014 11:30:50.103 SophosWebIntelligence[63]: tcp_connection_handle_destination_prepare_complete 2477 failed to connect
01/08/2014 11:30:50.106 SophosWebIntelligence[63]: tcp_connection_destination_setup_socket_events 2477 kqueue() failed 24 - Too many open files
01/08/2014 11:30:50.106 SophosWebIntelligence[63]: tcp_connection_handle_destination_prepare_complete 2477 failed to connect
01/08/2014 11:31:08.619 SophosWebIntelligence[63]: tcp_connection_destination_setup_socket_events 2490 kqueue() failed 24 - Too many open files
01/08/2014 11:31:08.620 SophosWebIntelligence[63]: tcp_connection_handle_destination_prepare_complete 2490 failed to connect
01/08/2014 11:31:08.623 SophosWebIntelligence[63]: tcp_connection_destination_setup_socket_events 2490 kqueue() failed 24 - Too many open files
01/08/2014 11:31:08.623 SophosWebIntelligence[63]: tcp_connection_handle_destination_prepare_complete 2490 failed to connect
01/08/2014 11:31:08.657 SophosWebIntelligence[63]: tcp_connection_destination_setup_socket_events 2491 kqueue() failed 24 - Too many open files
01/08/2014 11:31:08.657 SophosWebIntelligence[63]: tcp_connection_handle_destination_prepare_complete 2491 failed to connect
01/08/2014 11:31:08.660 SophosWebIntelligence[63]: tcp_connection_destination_setup_socket_events 2491 kqueue() failed 24 - Too many open files
01/08/2014 11:31:08.660 SophosWebIntelligence[63]: tcp_connection_handle_destination_prepare_complete 2491 failed to connect
01/08/2014 11:31:08.712 SophosWebIntelligence[63]: tcp_connection_destination_start failed to create socket(2) 24 - Too many open files (sandboxing issue?)
01/08/2014 11:31:08.713 SophosWebIntelligence[63]: tcp_connection_destination_start failed to create socket(2) 24 - Too many open files (sandboxing issue?)
01/08/2014 11:31:48.169 apsd[255]: Unrecognized leaf certificate
I don't know exactly when it started, as I only notice the problem when trying to open a new webpage, but I'm pretty certain it was within this range.