Unfortunately there could be many causes for premature battery death. The top culprits in ALL cars would be a bad alternator that isnt putting out proper charge to recharge the battery, a bad battery itself (if yours is factor and never changed then its time), or you could have poor connections. Then there are some GM specific things such as a bad Brake Control Module, Bad Fuel Pump, etc. Lets start with easiest first. If you are not handy or dont feel comfortable under your hood then there are alternates to the below
1. Check the battery cables at the battery posts (yours is side mount) and make sure they are tight, wont wiggle or twist back and forth. If they do tighten them
2. Check the alternator wires to make sure they are firmly attached, no loose nuts or bolts, etc. Tighten but dont over tighten and strip or break
3. Check for corosion on battery, battery tray, battery cables. These can drain the battery. If you have corosion then you can purchase CRC battery cleaner with Acide detector at local parts store to spary and clean.
4. At night go to your car and see if any lights, such as glove box, trunk, hood, dash, etc are staying on. Sometimes trunk or glove box lights stay on but since we dont look in either often we dont notice.
5. Crank the car and have someone stand in front as you are in the drivers compartment. Turn your lights on and then bright. Depress the brake pedal and ask the person if the lights dim or flicker at all. Also look at your instrument panel and see if your lights there are pulsing, etc. This can indicate a bad alternator
6. Turn on radio and see if you hear a hum (not static) but a low hum or whine. This could be a bad alternator.
An alternator has DIODES in it and they can go bad causing it to fail.
An alternative to above is to take it to your local Autozone, Advance, Napa, or Oreilly auto parts store and they can do a "load check" on the battery and alternator to see if they are functioning properly as well.
Now for the GM issues.
GM cars are known, even the Corvettes and Cadillacs, as having bad fuel pumps, Climate control, and ABS sensors.
1. ABS control module can go bad. A common diagnosis is to listen and see if you hear a hum comin from middle to rear of car on drivers side, near rear wheel well, CAR OFF. If the car is off and you hear this hum. Its possible the ABS module is bad and will need to be replaced. They are very expensive to replace unless you find a reputable place to have yours rebuilt. If you are a GOOD DIY person and comfortable with cars a good site is www.absfixer.com
. You can disable the ABS module by pulling a fuse in the engine fuse block. Im not sure the diagram for your model. Check your owners manual.
2. Fuel pumps can also go bad and continuously run. If its running it will drain a battery. You may not have symptoms in the running of the car if fuel pressure isnt affected. Listen for a similar him in same area (mid to rear) of car. Hum will be with car OFF
3. Climate control in your Caddy is very advanced and uses a climate control module and not typical switches and wires. All computerized. If you've noticed a change in performance of your fan output (low air output or higher output at lower settings) Change in air temperature and temp not matching what you have set on the control Cold=Cold.. Hot=Hot.. then its possible this is a drain.
Unfortunately the last three are somewhat easy to diagnose, but hard to fix. YOu will require a good mechanic or your dealer for these repairs.
FYI.. the same site for your brake module rebuilds teh climate controls as well.