This article is from the Star Trek Tech FAQ, by Joshua Bell inexorabletash@hotmail.com with numerous contributions by others.
When the power on the receiving end of the transport failed, the
transport computer on the Enterprise was unable to maintain the
pattern integrity of the matter stream. This is akin to catastrophic
degradation of the pattern. Kirk said "Boost your matter gain, we need
more signal!" - perhaps indicating that the ACB could have been used
to reconstruct the pattern. In any case, the hand-off appeared to have
been nearly complete when the transportees began reforming on the pad.
Since the Enterprise could not handle the transport, the matter stream
was sent back to Starfleet HQ, in the hopes that enough of the pattern
remained in the ACB to reconstruct them at the sending site. It
wasn't, and the subjects died shortly thereafter.
 
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