Fort Dawngaurd has chests on the first floor, in the hall opposite the training rooms and the dog kennels.
Ive used them from start to finish whilst doing the Dawnguard quests, they dont reset.
This isn't massively helpful though, some containers have a 30 day (game days) reset, like the barrels outside the Warmaidens in Whiterun.
Unless you (or anyone) would be willing to test out the containers by waiting 30+ days then checking, I would do it myself but I'm away from my Xbox for a bit.