I managed to reproduce the problem today (using Ubuntu 11.04 _without_ natty-updates). It seems the root cause may be a bug in ALSA after all. PulseAudio complained in syslog:

Jul 11 11:47:16 leon pulseaudio[1810]: alsa-util.c: snd_pcm_avail() a retourné une valeur qui est exceptionnellement large : 2922048 octets (15219 ms).
Jul 11 11:49:31 leon pulseaudio[1810]: alsa-util.c: Il s'agit très probablement d'un bogue dans le pilote ALSA « snd_hda_intel ». Veuillez rapporter ce problème aux développeurs d'ALSA.
Jul 11 11:49:31 leon pulseaudio[1810]: alsa-util.c: snd_pcm_dump():
Jul 11 11:49:31 leon pulseaudio[1810]: alsa-util.c: Hardware PCM card 0 'HDA Intel' device 0 subdevice 0
Jul 11 11:49:31 leon pulseaudio[1810]: alsa-util.c: Its setup is:
Jul 11 11:49:31 leon pulseaudio[1810]: alsa-util.c:   stream       : PLAYBACK
Jul 11 11:49:31 leon pulseaudio[1810]: alsa-util.c:   access       : MMAP_INTERLEAVED
Jul 11 11:49:31 leon pulseaudio[1810]: alsa-util.c:   format       : S16_LE
Jul 11 11:49:31 leon pulseaudio[1810]: alsa-util.c:   subformat    : STD
Jul 11 11:49:31 leon pulseaudio[1810]: alsa-util.c:   channels     : 2
Jul 11 11:49:31 leon pulseaudio[1810]: alsa-util.c:   rate         : 48000
Jul 11 11:49:31 leon pulseaudio[1810]: alsa-util.c:   exact rate   : 48000 (48000/1)
Jul 11 11:49:31 leon pulseaudio[1810]: alsa-util.c:   msbits       : 16
Jul 11 11:49:46 leon pulseaudio[1810]: alsa-util.c:   buffer_size  : 96000
Jul 11 11:49:47 leon pulseaudio[1810]: alsa-util.c:   period_size  : 48000
Jul 11 11:49:48 leon pulseaudio[1810]: alsa-util.c:   period_time  : 1000000
Jul 11 11:49:48 leon pulseaudio[1810]: alsa-util.c:   tstamp_mode  : ENABLE
Jul 11 11:49:48 leon pulseaudio[1810]: alsa-util.c:   period_step  : 1
Jul 11 11:49:48 leon pulseaudio[1810]: alsa-util.c:   avail_min    : 95617
Jul 11 11:49:48 leon pulseaudio[1810]: alsa-util.c:   period_event : 0
Jul 11 11:49:48 leon pulseaudio[1810]: alsa-util.c:   start_threshold  : -1
Jul 11 11:49:48 leon pulseaudio[1810]: alsa-util.c:   stop_threshold   : 1572864000
Jul 11 11:49:48 leon pulseaudio[1810]: alsa-util.c:   silence_threshold: 0
Jul 11 11:49:48 leon pulseaudio[1810]: alsa-util.c:   silence_size : 0
Jul 11 11:49:48 leon pulseaudio[1810]: alsa-util.c:   boundary     : 1572864000
Jul 11 11:49:48 leon pulseaudio[1810]: alsa-util.c:   appl_ptr     : 394960
Jul 11 11:49:48 leon pulseaudio[1810]: alsa-util.c:   hw_ptr       : 1152000
Jul 11 11:50:10 leon pulseaudio[1810]: alsa-util.c: snd_pcm_delay() a retourné une valeur qui est exceptionnellement large : -42434976 octets (-221015 ms).
Jul 11 11:50:10 leon pulseaudio[1810]: alsa-util.c: Il s'agit très probablement d'un bogue dans le pilote ALSA « snd_hda_intel ». Veuillez rapporter ce problème aux développeurs d'ALSA.
Jul 11 11:50:10 leon pulseaudio[1810]: alsa-util.c: snd_pcm_dump():
Jul 11 11:50:10 leon pulseaudio[1810]: alsa-util.c: Hardware PCM card 0 'HDA Intel' device 0 subdevice 0
Jul 11 11:50:10 leon pulseaudio[1810]: alsa-util.c: Its setup is:
Jul 11 11:50:10 leon pulseaudio[1810]: alsa-util.c:   stream       : PLAYBACK
Jul 11 11:50:10 leon pulseaudio[1810]: alsa-util.c:   access       : MMAP_INTERLEAVED
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   format       : S16_LE
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   subformat    : STD
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   channels     : 2
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   rate         : 48000
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   exact rate   : 48000 (48000/1)
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   msbits       : 16
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   buffer_size  : 96000
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   period_size  : 48000
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   period_time  : 1000000
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   tstamp_mode  : ENABLE
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   period_step  : 1
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   avail_min    : 95617
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   period_event : 0
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   start_threshold  : -1
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   stop_threshold   : 1572864000
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   silence_threshold: 0
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   silence_size : 0
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   boundary     : 1572864000
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   appl_ptr     : 406192
Jul 11 11:50:11 leon pulseaudio[1810]: alsa-util.c:   hw_ptr       : 11088001
Jul 11 11:54:18 leon pulseaudio[1810]: module-alsa-card.c: Failed to find a working profile.
Jul 11 11:54:18 leon pulseaudio[1810]: module.c: Failed to load  module "module-alsa-card" (argument: "device_id="29" name="platform-thinkpad_acpi" card_name="alsa_card.platform-thinkpad_acpi" tsched=yes ignore_dB=no card_properties="module-udev-detect.discovered=1""): initialization failed.

The snd_pcm_avail() and snd_pcm_delay() values were definitely bogus... So I'm starting to suspect that a "small" bug in VLC triggers the issue, but the real problem lies in ALSA?