Why was Dave harnessed back into the dog team even though he was known to be ill?

As sick as he was, Dave did not want to run freely behind the sled, he wanted to run is his own place.... to do his job. The men took pity on him and allowed him his place in the formation, so that he could die happy, doing what he loved to do.

Also, they held it a mercy, since Dave was to die anyway, that he should die in the traces, heart-easy and content. So he was harnessed in again, and proudly he pulled as of old, though more than once he cried out involuntarily from the bite of his inward hurt.