Maybe the problem isn't that it's 'draining' ..but that it's not charging ...for a period. (bad cable connections/grounds/battery/etc)? Like NJ_Mopar said above (good call). If your battery has gone low a number of times it's strength could be compromised by now. That's one thing batteries don't like is repeated depletion (leads to sulfation of the lead plates). Just an idea. If you had a real-time scanner you could plug into your OBD port you could check it when you are driving.
Could be something as simple as a loose or glazed drive belt (or glazed alt pulley).
Long boring story:
I once had a Land Rover and it would charge great sitting/idling all day long, or driving around town at lower speeds. But going down the highway at hwy speeds, and esp driving at night with the lights on, the alternator resistance was just enough to cause the alternator pulley to start slipping. If I drove home at night, the battery would be depleted the next am. And also the dash cluster acted like it was possessed because the battery was low and not charging. The previous owner had taken the cluster apart a couple times and replaced it (why I got it cheap). But if I drove home and ran some errands around town, esp if it was during the day (which was most of my driving), the battery would charge up (slower engine speeds=less alt belt slippage) and it would start fine the next morning. So most of the time it started in the mornings, but sometimes it wouldn't.
This flummoxed the previous owner, his mechanic, myself and some others. I even had the alternator rebuilt, then re-tested (new battery/cables too). One day, a different alternator guy (second alternator shop) noticed right away the alternator pulley was pretty glazed and partly worn down (sharp ribs). Nothing wrong with the alternator though. I replaced the pulley with a new one and a new belt, and it's charged great under all driving conditions ever since (15+yrs ago) ...never had another problem again. And I've driven that thing out to the mountains and off-roading a few times.
The point I'm making is there could be other things, simple things, which are often overlooked which might be causing your issue. Sometimes it's the smallest issue that can spoof larger, expensive, head-scratching problems. Its not something a mechanic is going to find with his scanner.
