Partly because the values of resistance/etc. in the various paths limit the currents needed to kickstart the switching process, so below a certain voltage there isn't enough to get it going. That's part of why they will often only start at a significantly higher voltage than they will continue to run at after startup.
Another issue is that if you run it at a lower voltage, it takes more current to create the same power, and thus the same output voltage/current ability. If teh device is capable of sucking more power from the lower-voltage source than it would have from the higher voltage source (most likely), then it will put more strain on all the current-carrying components for that power.
Say you've got input diodes in it that are rated for only an amp, and at it's nominal "low voltage" operation of 100VAC it gets that full amp thru them. At a lower voltage it's now going past the spec on those parts, which they might or might not tolerate. Usually it's not an issue, as the parts tend to be spec'd better than that, but not always. Cheaper is always better in these kinds of things.
Probably lots of other reasons I either am not aware of or cant' think of right now.
One more thing to think about is the total wattage output of the adapters: If they say theyr'e rated for up to 100W, for instance, that means 100W at the nominal input voltage. At a lower voltage (DC or AC), it probably won't be able to provide the same power level, and it probably doesn't fall off linearly, but faster than that, though I am not sure of the math.
I started experimenting wtih this stuff when I started on my CFL headlight/taillight setup, and have continued periodically since then with abotu the same results each time. Only time I have had real problems with them, or burned them out, is running on really low voltages after startup, like starting them on 40V and running down to 20V or something. They don't like to run that far below their kickstart voltages, in the case of the tiny little celphone chargers, sometimes.
Laptop adapters or other larger bricks tend to be more forgiving, but they also tend to require higher start voltages to begin with.
Anyway, usually if it says something like "input power 100-220VAC, 50-60hz", it'll probably also work on DC at some voltage level.
