Would a craft travelling increasingly close to the speed of light appear to be decelerating? I've been pondering the implications of time dilation. Is it right to assume that if a craft was travelling at a speed very close to the speed of light (>= 0.9999c for example), that to an external observer it would appear to be moving very much slower?
Example: at 0.9999c, time dilation is 70.71, so while the craft is travelling at 186,263.37 miles/s, doesn't that mean to a (stationery) observer it's only moving at 2,634.10 miles/s?
And at 0.99999c, time dilation is 223.61, so while the craft is now travelling at 186,280.14 miles/s, doesn't that mean to the observer it's now only moving at 833.07 miles/s?
The obvious implication is that as the craft approaches the asimptote of the speed of light, external observations (beyond around 0.9c) see it decrease in velocity towards the asimptote of being stationary.
Is this reasoning correct?
 A: No.
Time-dilation is the slowing of time as experienced by the fast moving craft, not the 'stationary' observer.
Remember that light moves at c, and we see it move at c, not some slower or stationary speed.
As the craft approaches c, it appears to accelerate increasingly slowly; from 0.99999c to 0.999999c is only a difference of 2.7 km/s, but it is still an increase in speed and thus an acceleration.
A: 
that to an external observer it would appear to be moving very much
  slower?

I don't understand the reasoning here.  When you write

assume that if a craft was travelling at a speed very close to the
  speed of light

I take that to mean that the craft is travelling very close to the speed of light according to an external observer.
Keep in mind that the craft is at rest with respect to itself and the specified velocity of the craft is the relative velocity between the craft and another inertial reference frame, i.e., an external observer.  In other words, according to someone inside the craft, it is the external observer that is moving very close to the speed of light.
So, when you specify the many speeds in your question, your actually specifying the speed of the craft according to this external observer.
To summarize, you're:
(1) asking us to assume that a craft is travelling at a speed very close to the speed of light [according to some observer]
(2) and then asking if it would appear to be moving much slower to this same observer
to which the answer is, of course, no.
A: "I've been pondering the implications of time dilation. " - thar be dragons! :)
The answer to the question is no, of course. Per the previous answers you have to consider frame of reference which in space time is arbitrary. Time dilation is how you resolve the problem of two objects traveling directly towards each other at > .5C per a 'stationary' third reference point. If each is traveling at > .5C then Newtonian physics says that the speed of one relative to the other must be > 1C. That's not possible because of the time dilation. 
