The other thing to consider, Josh, is it an extended drop in power or is it a flutter? The reason is a cap will discharge rather quickly. They're only used for quick compensation (such as a bass hit in your stereo) and not really designed for keeping something at 14.4v constant for longer than a minute or two at the most. Once the reserve is gone then it's just going to flow straight from source to output, so whatever comes in goes straight out.