I'll put forth a hypothesis as to why the SE is more susceptible to these failures than the higher end models... The SE does not have the Ford My Touch Electronics system, correct? So with that missing, and maybe a few other less fancy power consuming options, it probably has a significantly _smaller_ current load on the 12 V system. Am I correct in assuming that most of the electrical equipment in the vehicle runs off the 12 V system regardless of whether the vehicle is on or off? Restated, everything runs off the 12 V system, and the 12V is fed by the DC/DC converter from the HV battery as required. Right?
That's a lot of current to supply. So the DC/DC is a pretty high current output device. Right? (Anyone know it's output current rating and/or architecture, i.e. PWM or zero-crossing type?) I will assume that Ford hasn't done anything fancy with the systems design of that device, and used a single converter (although the converters are getting pretty sophisticated these days). Most DC/DC converters require a minimum load to operate nicely, and are not designed to handle a really wide range of load currents. They may be optimized to handle the heavy current load well, but at some compromise to the low current end of performance. I'll assume that Ford chose (logically) to optimize the performance at the high-current end of operation. The voltage output, the voltage ripple, and the switching noise (in the case of a PWM system) all vary as a function of load current. I'm going to speculate that the SE current draw is frequently low enough that when the vehicle is trying to charge the battery, the DC/DC converter is only marginally nice about some aspect of it's output; maybe it's output voltage is not well regulated, either a bit too high or low, or the voltage noise and ripple on it is too large. All of these deviations would be bad for a lead acid battery over time.
Too high a voltage will corrode the positive plate of the battery and lead to premature capacity failure (and also electrolyte loss). Too low a voltage will undercharge the battery, lead to sulfation of the negative plates, and again premature capacity failure of the battery. Too much voltage ripple, and you might get both symptoms.
My speculation is the the extra current draw of the systems in the SEL and fancier models puts a heavier load on the DC/DC converter, and thereby puts that converter into a more favorable portion of its design window (higher current output) where it operates more efficiently and with better tolerances on its output voltage, voltage ripple and noise. The lighter load of the SE vehicle may put the DC/DC converter close to its lower current limit on decent operation where it fails in some way to keep the battery properly charged.
This hypothesis might be tested by putting an oscilloscope on the 12 V system and recording not only the DC value of voltage, but also the ripple and switching noise on it as well. Just a hypothesis.... (Note that this issue is independent of the other issue that kaptnk228 experienced which may be the unwanted resistance in some cable connector or fuse somewhere in the charging system which probably also lead to the prolonged undercharging and capacity loss of his battery.)
I'll also take a stab at why the failures occur primarily overnight, and not after just a couple hours in the parking lot at work... If the vehicle is not charging the battery properly, and the battery is progressively losing capacity over time, then the normal drains on the battery as the vehicle periodically uses current in the off state (as people have seen) become a more serious challenge for the battery. Now assuming the vehicle experiences more total "wakeup and use some current" events over an 8 hour night than a 2 hour stop at the shopping mall, then the first time the battery will fail to hold sufficient voltage to boot the vehicle is naturally going to occur after the longer overnight string of drains rather than just a 2 hour string of drains (regardless of whether these drains are normal or otherwise). It's simply a consequence of the slowly diminishing capacity of the (12V) battery.