Could someone explain this to me? Why don't the U.S. go after the domain name?
There has been no evidence that the US government was involved in these recent events:
* The ending at 24 hours notice of WikiLeaks' DNS arrangements with Everydns.net
* The sudden termination of WikiLeaks' hosting on the Amazon EC2 cloud service
* The massive (ongoing) DDoS attack against WikiLeaks
WikiLeaks has reportedly been offline three times since this affair began, and today has only been accessible by IP address or through mirror sites.
While there has been a public call made by Senator Joe Lieberman, chair of the Senate Homeland Security Committee, for US companies to terminate any agreements with WikiLeaks, this does not constitute action by the US government.
Likewise, none of the statements branding WikiLeaks a "terrorist" organisation or calling for the "execution" of Julian Assange have been made by the US government.
So one answer to your question might be "because they don't need to".
In any case, the controversial data archive has already been spread "to over 100,000 people in encrypted form" according to Mr Assange, and will apparently be released automatically if WikiLeaks is somehow shut down.
So another answer to your question might be "because it will not change anything".
Mr Assange is currently in England and has not been charged with any offence.