Are you amplifying from a cDNA library? A cDNA library which is constructed using only poly(T) primers is biased towards amplifying only the 3' sides of the RNA library, especially for longer sequences. Use of random hexamers in combination with poly(T) can prevent this. There is to my knowledge no other general rule that states you should amplify only towards the 3' side of genes.
What gene are you looking at and what do you want to do woth it? Could be that this part of the gene simply contains the functional domain of the protein it encodes and as such is the most conserved/interesting for your experiment.