If the black batteries you have are protected (AW?) batteries, it could be that the current draw is increasing as the voltage drops and it's tripping the protection circuit. It seems crazy to me that either of those two lights are pulling that much current from the battery though.
Are you fully charging the batteries? What's the ending voltage when you take them off the charger?
I have the QB2L-X (original version, without burst), and the original D25LC2. I would not recommend using a pair of 16340 batteries in either of them. I like to use a 17650 battery (Eagletac) battery in the QB, and a 18650 battery in the D25LC2, for much better run times, and fewer headaches (fewer batteries to charge, at one time).
I'm pretty sure the OP is referring to the Eagletac 16340 protected battery in the picture (far left:
Not my greatest picture, but...
You may want to top off your 16340 batteries, every month or two, even if you don't use them regularly, so they're at their peak charge, when you do need them. They're good quality batteries, and they should easily be able to keep up with your lights, unless you've already charged them hundreds of times, and they're not holding a charge as well as they used to; but cut-off after only two or three minutes, should not be occurring, even if that were the case.
Eagletac lithium ion batteries were the first nice (high quality) batteries I ever purchased.
Both of those lights have mechanical switches, so I don't believe there should be any parasitic drain to worry about - but I could be wrong.
How long have you had your 16340 Eagletac batteries? How often do you check your battery voltages, in unused lights? I only ask this because, if you're exposing them to more extreme operating temperatures (severe cold, especially), they may not hold up/perform as well as primaries/disposables, when not used, for long periods. That's the lithium ion battery's one weakness.
The D2 is a pretty decent charger. I have a couple of D4s, and some other XTARs (VP2, VC4). They all work great. On my D4s (probably on the D2, as well), there's a setting (if you press and hold the
Mode switch, while the battery's in it), that switches the charging circuit over, to accommodate a LiFePO4 battery, which charges at a lower termination voltage than regular lithium ion (ICR) batteries. If you managed to switch it over to that, your batteries wouldn't be getting the full charge they should be getting, but would look as if they're fully charged. That's the only other thing I can think of, with the charger, possibly being the issue.