While doing all my wc3270 testing for my dropout problem (topic "Problem setting up new userid"), I seem to have come across a way to logon with reconnect. So far I've had a 100% success rate logging on with reconnect, and I've had a lot of reconnects with all the dropout problems.
It involves turning off TN3270E support (which didn't help with the dropout problem, but seems to have helped with the reconnect problem). Using wc3270, the command to connect to FanDeZhi is
wc3270 n:xxxxxx.yyyy.com:zz
xxxxxx.yyyy.com is FanDeZhi's web site, and zz the port to connect to. The "n:" tells it to turn off TN3270E support.
I don't know whether other 3270 emulators allow this, or how to do it.
Of course it's possible that turning off TN3270E support might have undesirable consequences. However I haven't come across any yet, and using ISPF seems to be unaffected.
There's a document here (https://tools.ietf.org/html/rfc2355) describing TN3270E. It's pretty technical and I soon gave up trying to wade through it, but others might be interested.
Tim