In my HTML page I have 2 select menus with IDs \"month\" and \"day\" - \"day\" is empty when the page loads, \"month\" has 12 options with values 1-12 corresponding to Janua
This is a known issue for IE.
KB article with workaround: http://support.microsoft.com/kb/276228
Also: dupe of: innerHTML replace does not reflect
EDIT: Here is my working sample based on your code:
Selects January February March April May June July August September October November December