Android phone has Wi-Fi troubles after subnet change
Turns out it was a problem with the DNS servers my DHCP was serving up.  The first two were local DNS servers.  I don't know why they weren't working for android (they worked fine for the laptop computers), but as soon as I replaced the second local DNS server with a remote DNS server, things started working.  It also appears that android only pays attention to the first two servers given by DHCP since I had other servers listed after my local server.

It seems kind of fishy that only the android phones had problems with the local DNS server.  I wouldn't mind finding out what the underlying problem is, but changing the DNS servers is an acceptable workaround.