How close does the dip in traffic correlate to the new site design going live? Was it just a re-skin or did URL paths and/or content on the site actually change? In addition to checking your Google Analytics (or equivalent) Id check Webmaster Tools for the Search Analytics report to see if any loss in traffic from specific keywords can be tallied back to the site launch. This could be more of a technical issue than a content one if so.
It could still be external factors of course, have you been tracking any of your competitors, have they been more active of late?
Losing traffic is very different to struggling to get traffic in the first place, so thanks for clarifying!