Torchwood was formed to defend against the Doctor (10th Doctor episode Tooth and Claw), not to work with him. It's only in the final days of the Torchwood Institute that they aren't predominately working counter to the Doctor, so there's not a lot of incentive for him to be stopping by to help them out.

In the later days, of course, there was more attachment, with various companions working for/with Torchwood. However, we've seen that once a companion leaves the Doctor, he moves on, and this is especially true once he regenerates. We've seen mixed feelings towards Jack in particular - he often doesn't agree with the way Jack does things, and he's not totally comfortable with the fact that he ended up immortal through their time together (with Rose).

It seems reasonable to assume that the 11th Doctor doesn't feel any special need to assist Torchwoord, so it would only be if he wanted/needed to help Earth itself. However, the Doctor doesn't solve every problem in the universe (he's busy enough solving the ones he caused!); let alone all the ones that exist on Earth.

Also, from all appearances, most of the time when the Doctor shows up and solves a crisis, it came about by accident - he happened to turn up at a fortuitous time. We see a few deliberate journeys, but they are in the minority; it's possible that these aren't as accidental as they appear, of course, but the evidence is that he fixes things as he finds them - he's not Sam Beckett seeking to right what once went wrong.

So he's not really keeping an eye out to help Torchwood, and he didn't happen to blunder into Miracle Day, so the question is whether he would have been called to help somehow. Even if he was, since the 9th Doctor, we've had many mentions of "fixed points in time":

Fixed points were events and/or individuals who had such long-standing impacts on the timeline that no one, not even Time Lords, dared interfere with their natural progression. The Doctor, free to interfere in alien invasions and save planets in most cases, could neither interfere nor interact with these fixed points. Were a fixed point to be interfered with, the change would be circumvented, making the timeline continue despite changes.

It's possible that Miracle Day (and other things Torchwood has dealt with) was a "fixed point". (However, Jack does say that the future is "still being written", and if it was a fixed point, there's a chance that he would know about it given his history). If it was, then there would be nothing the Doctor could do anyway.

Finally, it's possible that the Doctor was involved, and we just never saw it. He's had around 1,000 years of life (and presumably more that we haven't seen anything of yet) and we only get glimpses of small parts of this. Perhaps the Doctor (any incarnation, really) nudged a few vital pieces into place, without Torchwood (or us) knowing anything about it, while he was having some other adventure on Earth in mid 2001.

Torchwood was formed to defend against the Doctor (10th Doctor episode Tooth and Claw), not to work with him. It's only in the final days of the Torchwood Institute that they aren't predominately working counter to the Doctor, so there's not a lot of incentive for him to be stopping by to help them out.

In the later days, of course, there was more attachment, with various companions working for/with Torchwood. However, we've seen that once a companion leaves the Doctor, he moves on, and this is especially true once he regenerates. We've seen mixed feelings towards Jack in particular - he often doesn't agree with the way Jack does things, and he's not totally comfortable with the fact that he ended up immortal through their time together (with Rose).

It seems reasonable to assume that the 11th Doctor doesn't feel any special need to assist Torchwoord, so it would only be if he wanted/needed to help Earth itself. However, the Doctor doesn't solve every problem in the universe (he's busy enough solving the ones he caused!); let alone all the ones that exist on Earth.

Also, from all appearances, most of the time when the Doctor shows up and solves a crisis, it came about by accident - he happened to turn up at a fortuitous time. We see a few deliberate journeys, but they are in the minority; it's possible that these aren't as accidental as they appear, of course, but the evidence is that he fixes things as he finds them - he's not Sam Beckett seeking to right what once went wrong.

So he's not really keeping an eye out to help Torchwood, and he didn't happen to blunder into Miracle Day, so the question is whether he would have been called to help somehow. Even if he was, since the 9th Doctor, we've had many mentions of "fixed points in time":

Fixed points were events and/or individuals who had such long-standing impacts on the timeline that no one, not even Time Lords, dared interfere with their natural progression. The Doctor, free to interfere in alien invasions and save planets in most cases, could neither interfere nor interact with these fixed points. Were a fixed point to be interfered with, the change would be circumvented, making the timeline continue despite changes.

It's possible that Miracle Day (and other things Torchwood has dealt with) was a "fixed point". (However, Jack does say that the future is "still being written", and if it was a fixed point, there's a chance that he would know about it given his history). If it was, then there would be nothing the Doctor could do anyway.

Finally, it's possible that the Doctor was involved, and we just never saw it. He's had around 1,000 years of life (and presumably more that we haven't seen anything of yet) and we only get glimpses of small parts of this. Perhaps the Doctor (any incarnation, really) nudged a few vital pieces into place, without Torchwood (or us) knowing anything about it, while he was having some other adventure on Earth in mid 2001.