Ok, here is the thing:
I have 20 of them. Some are labeled "Funduino" and some "Arduino".
After I reboot my computer, all of the sudden ALL of them work the first time I connect them. If I disconnect and re-connect, about 10 will not be recognized by windows.
The thing is, if one is not recognized by my computer and I connect it to another, it still will not recognized...
Anyway, I am baffled...
I was pointed by Robert that the FT232R requires the TEST pin to be connected to GND. I tried to do that on one of the Arduinos that was "acting up" (i.e., first connection is successful but successive connections fail). That seems to make a successful connection every time.
This is not a workable solution for me since they are all soldered to my PCB and I don't have a the tools to remove them.
If this is the solution, why are the Arduino Nano schematics and design not updated?