The transporters in ENT were always much faster than the transporters in TOS. I always took that to mean that there was some additional aspect added to the transport process by the 23rd Century that made it slower: The bio-filters.
But there's no evidence that biofilters existed before the 24th century, and episodes like "Miri" and "The Omega Glory" suggest that transporters of the era didn't have the ability to filter out disease organisms. Not to mention "The Mark of Gideon." Would Kirk still have had Vegan choriomeningitis microbes in his blood if the biofilters edited them out?
So I figure, by the 23rd Century, they added bio-filters to the transporters, and that both slowed the process down and required the subjects to be relatively stationary (unless the transporter operator was really good, as in the new movie).
But in "Assignment: Earth," we were shown that transporters could beam up people in rapid motion so long as they were set to wide-beam. As others have stated, the far-from-ideal circumstances of the transport in the movie probably made it more necessary for the target to be still than would normally be the case. (After all, Spock in the Jellyfish was moving quite quickly relative to the Enterprise
when he was beamed aboard.)
My take on the transporter-lock problems in the film's Vulcan sequence is that the subjects moved after
the initial transporter lock had been established. With Kirk and Sulu, the transporters were initially targeted on the platform, and then once they fell off, the operator had to retarget the scanners and "catch up" with two people who were falling at terminal velocity, much faster than simple running, as someone said above. With Amanda, she moved after the transport had already been initiated. So the beam was calibrated to a stationary target, and since transport was already engaged, it was too late to reset when she fell out of the beam.