The auxiliary battery is contained within the siren module (two little NiMH cells); these tend to go bad and leak with age, ruining the whole siren module. Another common occurrence is moisture creeping in there and causing oxidation on the circuit board, leading to erratic behavior from the module (random triggers, silent alarms, random "no confirmation beep" when arming, door "alarm led" staying solid or blinking rapidly for several seconds before blinking normally when arming, etc), even if the siren unit itself looks brand new from the outside. I recently had to replace mine ('08 RS4 as well) for both these reasons. In most cases, a
VCDS/obd11 scan should reveal a "communication error with the siren module" and/or "alarm triggered by so-and-so latch" code. Do keep in mind that this module is "sealed from factory" and any attempt to pry it open for inspection will most likely be destructive in order to be successful.
Of course, prior to diving into potentially costly and time consuming research and repairs, the obvious first step is to ensure that all you door, hood and trunk (bonnet and boot

) latches are working properly (ie, sending the proper open/closed signal to the control module); a misbehaving door latch is often found to be the culprit when an alarm is randomly triggered for "no reason".
If all latches check-out, be advised that the dealers will ask an eye-watering amount of money for a diagnosing and replacing the siren unit (we're talking 4 digits when it's all said and done); there are Asian aftermarket alternatives (aka Chinese knock-offs) available, and the one I found on Amazon did the trick perfectly (99$ instead of the dealer listed 900+ for the part alone). The siren is tucked away in the the right rear quarter panel, hidden behind the side boot liner in sedans and avants, or through the soft top storage compartment in cabrios (work is done whilst the compartment lid is stopped "mid-course") ; It is a fairly easy DIY job (albeit perhaps not "sorted in a matter of minutes" if you take your time and are careful not to break any clips or fasteners...), no special tools needed (ratchet set, couple of torx bits and you're good to go), and several tutorials are available on YT.
Do stick with the oem part number on your unit as you might be tempted to go with physically identical models that only have a slight variation in the part number prefix (8K0 instead of 8L0 for example), don't do it; sure, they look the same and they're half the price, but sadly not compatible...pretty much the whole VAG fleet from late 90s to late 00s uses the same unit, but anything "B8 onwards" won't work, and any attempt to buy a used/salvaged unit is somewhat pointless by now as the "newest possible" ones are almost 20 years old!
Hope this helps