I didn't get any answers the first time around so I'll ask again!
The "Titanic: Honor and Glory" project maintains a view that the ship, after her fatal collision with the iceberg and a halt that lasted a couple of minutes, did indeed resume sailing at half speed for nearly ten minutes before her final stop, ordered by Captain Smith himself. I couldn't find any sources for this claim anywhere on their website and the debate on Encyclopedia Titannica (a message board/wiki for Titanic enthusiasts) is quite dated and didn't come to a conclusion.
Is there any evidence that this did indeed happen and if so, are there any speculations as for why? I'm a Titanic enthusiast myself but didn't come across this claim until a couple of years ago. If the ship did indeed resume sailing, I'm baffled that it isn't a publicly known fact as it would (at least in my opinion) demonstrate extremely bad judgment on Captain Smith's behalf that should have attracted some interest from the press at the time. I would imagine that moving the ship while she was so badly damaged must have made the situation even worse.
Thanks for any insights!
Can't help much to be honest, but I can link you to a thread where authors of a few books on Titanic discuss this matter.