While I think doubling based on time is just as valid as doubling based on mileage, I think you need to consider what race you are training for before you can get a good answer to the question of at what point you should be doubling in the first place.
If you are a slower runner running lots of half marathons, or maybe even 15ks or 10 milers, there is a real benefit to trying to get in runs of longer than one hour.
Mu easy distance pace is typically in the 6:40 to 7:00 range most days, so for marathon training, I would try to get as many ten milers in as possible, giving me lots of days near 70 minutes.
The purpose of this was to try to get my body to adapt to changing between sources of glucose. You draw glucose from your blood stream, your liver and the muscles which are being engaged. I have always understood that you run out of glucose from the first source (blood stream, I believe) after about an hour of aerobic exercise. Since races that go in excess of an hour will require you to utilize more than one source of glucose, it makes sense to get your body adapted to engaging those different sources. This, as many runs over an hour for me as possible, and I would not double until I got into the mid 80s or so for weekly mileage, and even then I would only double once a week.
If you are training for 5k/10k, I would agree wholeheartedly with Marco Brolo and use an hour as a break point.