Linc. I thought the problem had gone away, but after just four days it has returned.
The 'bouncing icon' problem started again today, and I made a note of the exact time as per your request. According to my radio-controlled clock it started at local time 14:32:20.
The bouncing icon -which happened to be Safari- continued bouncing until 14:34:10, then it stopped as before with the entire Mac side of my computer then becoming hung.
I had to perform a forced shutdown with the power button at about 14:36:00.
Following the restart I copied the lines from my Console log that covered the period when the icon was bouncing. (I hope I've not been too liberal in my selection.)
It means absolutely zilch to me, but clearly the thing that keeps repeating itself is the 'launchd.peruser' thing, and that in turn seems to relate to my AirPort BaseStation, (which is actually a Time Capsule back-up drive/router).
Have you any ideas as to what might be occurring from this?
Console log:-
03/10/2013 14:32:22.948 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent[40207]) Exited with code: 1
03/10/2013 14:32:22.948 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent) Throttling respawn: Will start in 10 seconds
03/10/2013 14:32:32.979 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent[40209]) Exited with code: 1
03/10/2013 14:32:32.979 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent) Throttling respawn: Will start in 10 seconds
03/10/2013 14:32:43.011 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent[40212]) Exited with code: 1
03/10/2013 14:32:43.011 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent) Throttling respawn: Will start in 10 seconds
03/10/2013 14:32:53.041 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent[40214]) Exited with code: 1
03/10/2013 14:32:53.041 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent) Throttling respawn: Will start in 10 seconds
03/10/2013 14:33:00.432 coreaudiod[160]: Disabled automatic stack shots because audio IO is active
03/10/2013 14:33:00.491 coreaudiod[160]: Enabled automatic stack shots because audio IO is inactive
03/10/2013 14:33:03.075 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent[40216]) Exited with code: 1
03/10/2013 14:33:03.075 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent) Throttling respawn: Will start in 10 seconds
03/10/2013 14:33:13.107 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent[40219]) Exited with code: 1
03/10/2013 14:33:13.107 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent) Throttling respawn: Will start in 10 seconds
03/10/2013 14:33:23.141 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent[40220]) Exited with code: 1
03/10/2013 14:33:23.141 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent) Throttling respawn: Will start in 10 seconds
03/10/2013 14:33:33.173 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent[40223]) Exited with code: 1
03/10/2013 14:33:33.173 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent) Throttling respawn: Will start in 10 seconds
03/10/2013 14:33:43.206 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent[40225]) Exited with code: 1
03/10/2013 14:33:43.206 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent) Throttling respawn: Will start in 10 seconds
03/10/2013 14:33:53.238 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent[40226]) Exited with code: 1
03/10/2013 14:33:53.238 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent) Throttling respawn: Will start in 10 seconds
03/10/2013 14:34:03.271 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent[40228]) Exited with code: 1
03/10/2013 14:34:03.271 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent) Throttling respawn: Will start in 10 seconds
03/10/2013 14:34:13.301 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent[40231]) Exited with code: 1
03/10/2013 14:34:13.301 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent) Throttling respawn: Will start in 10 seconds
03/10/2013 14:34:23.334 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent[40233]) Exited with code: 1
03/10/2013 14:34:23.334 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent) Throttling respawn: Will start in 10 seconds
03/10/2013 14:34:33.368 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent[40235]) Exited with code: 1
03/10/2013 14:34:33.368 com.apple.launchd.peruser.501[223]: (com.apple.AirPortBaseStationAgent) Throttling respawn: Will start in 10 seconds