Had exactly the same prob on my 2004 X5 just over a year ago.
Changed the FSR but no change

It was the BMW genuine ipod connector in the rear compartment and the lead that went to the front for the HU. took ages to find as it was erratic.

We thought it was something to do with the door locks and starting the sat nav up but after they disconnected the lead, it has been fine ever since...well up to the point when I binned the original HU for a Hualingen 5gen + audison voce speakers + sub :-)

HTH

Well, two more things to scratch off the list. I disconnected the connector going to the radiator fan switch - still getting 4.2 amps of current flow. Same thing when I disconnected the connector going to the (aftermarket) ipod connector.

As far as checking whether the alternator is the culprit, what's the best way to do that? Will disconnecting the connector going to it be sufficient?

Any other common causes of a leak this size that I should check, before I go through the tedious exercise of removing each fuse one at a time? Thanks.

I had a '88 750il that the battery went low after a couple of days. I put a amp meter in line {in series} of the negative cable to the neg battery post and pulled each fuse one by one. When I pulled a fuse and lost the current draw, I checked all the devices wired into that circuit. Turns out it was the lock tumbler deicer. The switch that enabled it would stick. So put a amp meter on it and pull the fuses one by one and go from there. Check the "usual suspects" first, for sure.

I think trader4 made a good suggestion which would be to 'listen' to the car. As in, go for a drive, pull it into a garage at night and just listen to see if you can hear anything whirring away. Just remember these cars take up to 20mins to fully go to 'sleep', so if something persists beyond that.....

on the far wall in the trunk (remove spare tire) is another set of fuses. they are master fuses and great grand master fuse.... remove them one at the time, it will speed up the narrowing down the fuse tree...

Hvacdude,

Yeah, that's the path I'm on. I've pretty much ruled out the prime suspects, so I guess it's time to start pulling fuses one by one. I've already pulled each of the ones in the cargo area because they're a lot easier to get to, but no luck - still getting over 4 amps.

I have a question about this whole sleep mode thing. I disconnected the negative cable this past Sunday and fully charged the battery, and have kept the cable disconnected ever since. I assume this is plenty of time for the car to have gone deep into sleep mode. So when I reconnect the cable to the negative battery terminal (with a 1 ohm resistor between the terminal and the cable, across which I'm measuring the voltage drop), am I "waking the car up" and creating an unintended but normal drain? I've assumed that since my drain is so massive, the difference between the current draw in sleep mode, and that when the system is "woken up" is in the noise, but am I making a mistake with this assumption? Thanks.

i think with such massive drain the car can't go to sleep mode

as above, mine had a erratic current draw of nearly 4 amps. it took nearly a week in the garage with them pulling fuses one by one and leaving a tester on the battery which then had a printout of what times it spiked
The fault sounds identical to yours