According to the Gamepedia Wiki, witches drinking a potion when they're killed will drop that potion 8.5% of the time. Dinnerbone recently confirmed this on Twitter as well.

I did some testing, and I couldn't get any witch to drop a fire resistance potion ever. The setup was as follows: using command blocks, I spawned in one witch every second. They hit a tripwire, which pushed them with a slime block through a fire on a magma block, and then down into a hole where they were killed by fall damage. Hoppers collected their drops.

Using the /entitydata command, I was able to see that all the witches were, in fact, holding fire resistance potions. Additionally, they all had fire resistance particles when killed. And the NBT tags did include a 0.085 Hand Drop Chance, as expected. And yet after AFK'ing for long enough to fill a double-chest (plus hopper backup) with drops (about 20 minutes), not a single potion was dropped.

Doing the math, I had spawned over 1,200 witches, all of which were killed while drinking fire resistance potions. At an 8.5% drop rate, we should expect around 102 fire resistance potions, give or take some randomness. Zero is certainly not expected, and thus indicates there may be a bug preventing the potions from dropping properly.

I haven't tested with other potion types, but it certainly affects fire resistance potions.