I don't know how IntelliJ IDEA works with AS 7.1 but I do know the just released JBoss Tools M5 for Eclipse works fine with AS 7.1 CR1 with both debugging and launching.
My guess can only be that Intellij (like us) parses the standalone.xml and does not handle the new property format in AS 7.1 - if you can somehow force that in IntelliJ to use port 9999 or 9990 (dependent on what type of API intellij uses) then you can probably tweak it to work.
Otherwise try out M5 :) http://community.jboss.org/community/tools/blog/2011/12/23/jboss-tools-m5-is-coming-to-town