Dropping the blocking factor from models if it's not significant?

#1
What's everybody's thoughts on dropping a blocking factor from models? I have a professor that's a big fan of blocking in ecological field experiments. He's always encouraged us to include a block factor (if applicable) during the experimental design. If it's significant...great. If it's not, drop it. Is this sound sound statistical practice?
 
#2
I don't think it would be good to drop the blocking factor. The blocking design presents a restriction on the randomization. That is, you randomize treatments within the blocks. So, I would think dropping the block would lead to biased results. In a subsequent experiment would wouldn't consider the same blocking factor.