Thank you! Your answer set me on the right path.
I changed device to devices.Current as you suggested and also removed the definition of the innermost XPathNavigator, as the value of issue is the InnerXml. The code that works is:
XPathNodeIterator devices = MainDataSource.CreateNavigator().Select("/root/device", NamespaceManager);
while (devices.MoveNext())
{
XPathNavigator device = devices.Current.CreateNavigator().SelectSingleNode("name", NamespaceManager);
if (device != null)
{
String deviceName = device.Value;
XPathNodeIterator issues = devices.Current.CreateNavigator().Select("/summary/issue", NamespaceManager);
while (issues.MoveNext())
{
String issue = issues.Current.InnerXml;
}
}
}