Recently I have had a myriad of problems with my beloved TT..  (2002 225hp, Roadster, w/Bose) I left it for about 2 weeks, came back and no start-- (battery corrosion on the terminals).  Jumped and it worked fine. 

- Now, I have noticed significant decrease in sound quality of the speakers.  (Sub is much weaker, other speakers sound flat)

- I have noticed the head unit backlight is flickering (never shutting off, getting brighter).

- Now my stereo (sound only) has started shutting off when I hit a bump in the road.  The head unit remains powered, and never goes to safe mode.  When this happens there is a clear clicking sound coming from the area of the amplifier (behind passenger seat). 

I read another forum positng which listed a similar problem with no solution -- (only that it was NOT resolved after replacing the amp or head unit).

PLEASE HELP -- Any advise would be really appreciated.

I had the same symptoms from the Bose system one my 2004 3.2 coupe. The sound would intermittently stop accompanied by the clicking noise that you described. Although I believe the clicking was coming trough the speakers. Replacing the amplifier corrected the problem. I can't swear to it, but it seems that the sound quality improved after the amp was replaced.