There is one thing that makes Dave want to keep pulling the sled even though he has gotten so weak -- his pride. Dave has always been a sled dog and that is his reasoning for being. If he cannot work, his purpose for living is taken away from him. He is like an athlete who does not want to retire even thought it is clear to everyone else that he can't get the job done anymore. Here is the quote that shows this most clearly:
For the pride of trace and trail was his, and, sick unto death, he could not bear that another dog should do his work.
You should note that Dave's attitude fits in well in this chapter. Early in the chapter, we see that Buck's pride will not allow him to see any other dog be the leader. He knows that is his place. Similarly, Dave's pride will not let him be taken out of the team. He knows that his place is pulling the sled and he does not want to be depirved of that duty.