Not sure this is relevant, but your command is running the site twice, mvn site will generate the site, and site:stage will also run the site, perhaps this is causing problems but I honestly can't see why.
Looking at the JXR documentation, it only mentions the site:site goal, I can't see why it wouldn't be run properly for the site:stage goal as it extends it. If you run the site goal, then copy the output to another directory, run the site:stage goal and compare the output it might give some insight into the problem.
Update: I tried this myself and the xref was included and aggregated nicely in c:\test\stage with the cross references correctly managed. I've included the configuration I used.
In my parent pom I defined the site configuration like this:
<build>
<plugins>
<plugin>
<artifactId>maven-site-plugin</artifactId>
<executions>
<execution>
<phase>prepare-package</phase>
<goals>
<goal>stage</goal>
</goals>
</execution>
</executions>
<configuration>
<stagingDirectory>c:\test\stage</stagingDirectory>
</configuration>
</plugin>
</plugins>
</build>
The distributionManagement section was configured with the site information (not really needed as I set the stagingDirectory above, but the goal won't run without it).
<distributionManagement>
<site>
<id>mojo.website</id>
<name>Mojo Website</name>
<url>scp://test/</url>
</site>
</distributionManagement>
My JXR configuration in the parent pom was as follows:
<plugin>
<groupId>org.apache.maven.plugins</groupId>
<artifactId>maven-jxr-plugin</artifactId>
<reportSets>
<reportSet>
<id>src-xref</id>
<reports>
<report>jxr</report>
</reports>
</reportSet>
<reportSet>
<id>test-xref</id>
<reports>
<report>test-jxr</report>
</reports>
</reportSet>
</reportSets>
<configuration>
<aggregate>true</aggregate>
</configuration>
</plugin>
The commandline run was mvn clean site:stage
Edit: Per the comments, there is a codehaus jxr plugin with slightly different semantics. Be sure to use the org.apache.maven.plugins version rather than the org.codehaus.mojo version.