Why has communism had such a lasting influence on human rights in China?

The reason for this is that communism is a system of
government that does not believe that individual rights matter to any great degree. 
Instead, it holds that the needs of the society are more important than individual
rights.

By communist theory, there needs to be a "vanguard
party" that will promote the cause of the proletariat and will fight against any
counterrevolutionary activity.  To communists, any activity that might work against that
vanguard party is counterrevolutionary and therefore bad for
society.

This is why China's government is so willing to
abridge the human rights of its people.  It feels that it is the vanguard party that is
protecting the rights of the proletariat.  Therefore, anyone who opposes it (whether it
be the Falun Gong or dissidents or whoever) is working to hurt the country as a whole. 
Such people must be suppressed where, in a democratic system, they would be allowed to
speak and act as they wish.