Last year one of the owners in my league gave up mid-year. He was in last place out of six teams and he simply cut off all communications and never submitted a starting lineup for the rest of the season. He had Green (QB), McAllister (RB), Moss (WR), and Gonzo (TE). If he had continued to believe in his team he most surely would have finished in third place and won all of his initial investment back (it was a money league, $100 per owner).
Here is some advice based on my 20 years of fantasy football:
Project the stats you think your players will accumulate over the entire season based on sound criteria. If you think you have a player you think will get you good numbers comparitively when it's all said and done, then keep starting him every week.
No doubt, you have to pay attention to what's happening. On the other hand, studs will usually produce in the long run no matter what. Their situation may inhibit them now and then but don't panic. If you got a play maker and your analysis of him is semi-accurate, then don't despair.
As Jimmy V. said, "Don't ever give up!".
Always do your homework!