I am creating a new issue for this because all the issues I found for this, and there are many, are all listed as resolved via workaround.
This is not resolved in 13w39b
I initially experienced this issue after upgrade to 13w39a. Rain would not stop, and did not respond to weather commands.
For a day, the issue went away. During this time it rained occasionally and then I was able to clear it with /weather clear.
Now the problem is back, it is raining and the rain does not respond to /weather clear or the toggle command.
Cannot recreate this issue, it is not a predictable problem. At some times the weather will respond to commands, and at others it will not and will be stuck until the server is stopped and reloaded.