I think part of the problem is that there are a large number of neglected teams that have an owner in name only. My strategy is to try to determine who is active by checking when home games are played, whether or not roster moves have been made, etc. Try to initiate trades with those owners and don't bother with the others.

I have made 29 trades (six teams) so far in 2006.
You can make it happen but it does take some effort to identify who is active.