What did me in is was that multiple unrelated software packages just happened to install adb.exe -- in particular for me (on Windoze), the phone OEM driver installation package "helpfully" also installed adb.exe into C:\windows, and this directory appears in %PATH% long before the platform-tools directory of my android SDK. Unsurprisingly, the adb.exe included in the phone OEM driver package is MUCH older than the one in the updated android sdk. So adb worked just fine for me until one day something caused me to update the windows drivers for my phone. Once I did that, absolutely NOTHING would make my phone status change from "offline" -- but the problem had nothing to do with the driver. It was simply that the driver package had installed a different adb.exe - and a MUCH older one - into a directory with higher precedence. To fix my installation I simply altered the PATH environment variable to make the sdk's adb.exe have priority. A quick check suggested to me that "lots" of different packages include adb.exe, so be careful not to insert an older one into your toolchain unintentionally.
I must really be getting old: I don't ever remember such a stupid issue taking so endlessly long to uncover.