I revisited the Malachite mine in Kynesgrove and the quicksilver mine in in Dawnstar and the ore does respawn, but I don't know how long it took. It may first appear that there is ore in the rocks, but it won't let you mine it. So I fast traveled to another city and back and then I could mine it again.
Also, if you want ore or ignits quicker, "wait" infront of a smith until they reopen their shop the next morning.
I think what is causeing all of this confusion is that the ore deposits out in Skyrim do not respawn. There is a deposit just to the left of the front door to Witerun, and I haven't seen that respawn EVER! But apparently the deposits in caves and dungens do respawn. Please correct me if I'm wrong.
Like I said...the one's in caves respawn...apparently in a about a month. But the one's out in the world dont. Beleave me, I'm have about 5 month's in game time pass and and one just to the right left of the whiterun door will not respawn. I check it all the time!
I do not think its a month. I think its more like 2 weeks. I mined ebony at the mine near the orc camp in the east, and did at the most 4 quests. That was on the 1st of Heartfire. It is the 14th, and the deposits are back. Maybe a glitch, maybe actual time. All I know is that it took 2 weeks, not a whole month.