I remember reading on some Audi forum about these cars using a "shake proof battery" . These cars are sprung pretty firm and Audi recommended a special battery that could withstand vibration. Audi claimed aftermarket batteries didn't last as long when used in the TT.
Fully charge and "high rate discharge test" the battery to see if the battery is actually OK. Have the alternator charge rate and diode pattern properly checked.
Check for parasitic draw. A car naturally draws some current from a battery to keep memory alive in the radio, computers and time clock so a very minute draw is normal. If something comes alive intermittently the battery will go dead over night or in a few days depending on the size of the electrical draw.
For piece of mind have the battery properly checked first.