The ace:dataExporter does not function when it is placed inside an ui:Repeat.
The "target" attribute of the ace:dataExporter is being used to identify the ace:dataTable containing the data to be exported, and this table is within the same form, but outside the ui:Repeat containing the dataExporter.
When trying to export data, a Server Internal Error happens (screen shots attached), and the below error is thrown in the server log.

4-Oct-2011 4:13:01 PM com.sun.faces.lifecycle.InvokeApplicationPhase execute
WARNING: Cannot find component "carTable" in view.
javax.faces.FacesException: Cannot find component "carTable" in view.
        at org.icefaces.ace.component.export.DataExporter.processAction(DataExpo
rter.java:104)
        at javax.faces.event.ActionEvent.processListener(ActionEvent.java:88)
        at javax.faces.component.UIComponentBase.broadcast(UIComponentBase.java:
769)
        at javax.faces.component.UICommand.broadcast(UICommand.java:300)
        at javax.faces.component.UIData.broadcast(UIData.java:1093)
        at javax.faces.component.UIViewRoot.broadcastEvents(UIViewRoot.java:794)

        at javax.faces.component.UIViewRoot.processApplication(UIViewRoot.java:1
259)
        at com.sun.faces.lifecycle.InvokeApplicationPhase.execute(InvokeApplicat
ionPhase.java:81)
        at com.sun.faces.lifecycle.Phase.doPhase(Phase.java:101)
        at com.sun.faces.lifecycle.LifecycleImpl.execute(LifecycleImpl.java:118)

        at javax.faces.webapp.FacesServlet.service(FacesServlet.java:593)
        at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(Appl
icationFilterChain.java:290)
        at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationF
ilterChain.java:206)