The Doctor has a new companion

[Broomstick]

It could also be he's done so much time traveling he doesn't know how old he is anymore. Rules or no rules he's doubled back over his own timeline multiple times. It may not have anything to do with trauma or whatever but simply that he's lost track. Or maybe he doesn't want to think about his age, just as he mostly seems to avoid thinking about the wife/mate and children we know he's had in the past but never hear anything about.

[Batman]

Or that. Again, only I know nuWho. I merely offered the potential trauma of regeneration as a possible explanation why the good Doctor seems to be a bit fuzzy about his age.

[Broomstick]

It's possible. Especially since the Doctor seems to find regeneration more traumatic than other Time Lords, or regeneration in other species like the Minyans of Minyos.

[Korto]

He said on at least one occasion in Old Who that regeneration affected his mind, in that it sent him into a manic phase, and even slightly crazed (something that I think we've also seen on occasion in NuWho). If it's had that affect, who's to say it couldn't have other, less visible effects as well?
Frankly, it would be a bit of a bugger with time travel keeping your age straight. It's not like you can say "I was born in X year, it's now Y year, therefore I'm Y - X old" I have to resort to working it out like that, and I'm nowhere near as old as he is.

[PREDATOR490]

I find it more likely the Doctor dosent know... because none of the writers know either however as far as in universe is concerned. It can easily be justified with the simple fact that counting age is a Earth thing which is based on Earth years.

Keeping track of time when your a time traveler is going to be hilariously difficult at the best of times without factoring in the Doctor is an alien that would logically only count his life in regenerations like we do.

At some point when you have lived for long enough age is going to become irrelevant compared to your own mortality. Which the Doctor is obviously having more issues with as he nears whats supposed to be the end of his regenerations.

[Eternal_Freedom]

An easy explanation for it is when Two explains to Victoria how old he is:

"Well, in your terms, strictly lineraly, about 450."

So there, his "age" already incorporates a fudge factor for correcting to human timescales. Heck, maybe his "900 year" comments as Seven and Nine were EArth years while Ten and Eleven prefer to count in Gallifreyan years for some reason.

[Lord Woodlouse]

I bet he says he's about 900 years old in the same way he calls himself John Smith. It avoids a more complicated answer.

[Patrick Degan]

Or it could be that he counts sometimes in terms of chronological years and other times in terms of his actual physiological age.

To give an example: the protagonist of Joe Haldeman's The Forever War, William Mandela, is by the end of the novel both 31 and 1174: the former being his actual physiological age and the latter being his chronological age counted from his date of birth and taking into account the number of years that piled up from relativity in all his star travel during the course of the war with the Taureans. He could give either figure as to what his age is and either answer would be correct. For the Doctor, all his time travel would have caused the years to pile up on him as well so that it would depend upon how many years, objectively, that had passed since his birth on Gallifrey and his subjective physical age. And after all those centuries, he'd be hard-pressed to know the exact figure without the TARDIS keeping track of his age for him and consulting the record.

[Bernkastel]

As someone who is mainly faimiliar with new Who, I really do hope that we are going to have an alien companion.

Concerning the age issue, I agree with Lord Woodlouse. I tend to assume he chooses the answer most suited towards the person asking about his age.