I tend to error check when using getElementById. I would expect that that is where your problem is.
Try this, and then test it in a debugger, but I will put an alert in.
var elem = document.getElementById(monthId);
if (elem.options) {
options[document.getElementById(monthId).selectedIndex].value
} else {
alert("elem doesn't have an options property");
}
You may want to not assume that the value property exists either, and do the same basic thing as I did here.
Once you get it working smoothly, where you know what is going to happen, you can start to remove the unneeded variables and go back to your original line, but for debugging, it is simpler to have one operation on each line and use separate variables, so that the debugger can show you what is happening.
You may want to understand the difference between undefined and null, and there are various pages on this topic but this one isn't too bad.
http://weblogs.asp.net/bleroy/archive/2005/02/15/Three-common-mistakes-in-JavaScript-2F00-EcmaScript.aspx