I have a 2006 Vanden Plas that every 2-3 weeks won't start. It acts like the battery is totally dead. When I purchased, I put a new battery and alternator in {5 months ago}, but this did not solve the problem. Took it to dealer and they said the battery was dead and charged..... Took it home and 1 week later same thing. Once I jump start, it does fine for the 2-3 week time period.
Noticed a clicking noise in the trunk fuse box. While not on the owners manual there appear to be 3 relays{?} in the box - 1 ++05164 2 B and 2 ++05167. Do any of these have to do with the battery starting system?

 

Sometimes relays that handle high currant loads will develop carbon on the contacts from arcing. Even though the coil will try to pull the contacts together the arcing will drive them apart so the result is a chattering noise. Large power relays can be disassembled and the contacts replaced. Small ones usually have to be replaced completely. My Corvette started having trouble running when first started. I replaced the MAF sensor. Didn't help. It has a relay that energizes at shut down to put currant through the sensor wire and clean it off for the next start. That relay was intermittent. A new one fixed the problem.

Whether one of those relays has anything to do with charging, I don't know. Someone that has dealt with that on your car may know. I would imagine someone will be along shortly to move this thread to the proper subforum.