You are running Byobu on a remote computer to which you have connected using PuTTY. Everything works fine, except that the Byobu commands that use function keys (like F2, F3 and F6 for example) do not work. This problem is caused because the sequences sent by PuTTY for function key press does not match what Byobu expects. This can be fixed easily in PuTTY.
Load the session you use to connect to the remote computer. Go to Connection → Data and set the Terminal-type string to putty-256color. Save the session.
Load the session. Go to Terminal → Keyboard and choose Xterm R6 in the Function keys and keypad section. Save the session.
Tried with: PuTTY 0.62 and Byobu 5.17