When I open a MS Excel file in Calc, it is opened correctly (specifically the colors of the sheet tabs on the bottom) and I make my changes to the sheets themselves, save it as the same type of excel file, and then reopen the document. When I reopen it, the formatting is different and there are no longer any colors on the sheet tabs at the bottom. Why is this? Is it a bug?
Based on your explanation, this behavior does seem like a bug. I believe that whatever features/nuances of an Excel file LO can import, LO can also export.
To file a bug, please follow the instructions here: https://www.libreoffice.org/get-help/bug/
(As an aside, LO 4.0 is dropping export support for some older MS-Office formats (6.0/95), so symmetric import/export will no longer be applicable. See here for details http://wiki.documentfoundation.org/ReleaseNotes/4.0)