I cannot "see" my 2nd gen iPod nano on iTunes 10.6 running on a new iMac with OS Lion.
I have worked through the various troubleshooters to no avail. Have Apple ceased to support the 2nd gen nano?
It does, I'll agree with you there.
I know this may seem like overkill, but perhaps it would be worth it to try and do a low level reformat of the iPod Nano's flash storage. There have been a few others in the past who have had this same issue and were able to resolve it by completing the reformat operation.
See this article for instructions on reformatting your iPod's HD in Mac OS X.