TheOptimizationIdiot - 8:31 pm on Mar 7, 2013 (gmt 0) [edited by: TheOptimizationIdiot at 8:37 pm (utc) on Mar 7, 2013]
WOW, now that's a question...
I would personally start with:
1.) User Behavior: Starting with patterns leading to the "slow drop". Have they changed wrt time on site, etc?
Is there something along the lines of previous availability of a product no longer available from the site? In other words: Stock level, back-ordered, discontinued. Even an order form not working (possibly only in certain browsers) that's causing people to keep searching rather than buying and ending the search?
Basically, actual behavior and any onsite changes that could cause a visitor to "search again after visiting" in order to find something they used to get from the site.
Or, in other words, is there anything to indicate "the search does not end" on the site(s) as often as it used to?
2.) Inbound Links: Previous link building efforts that have stopped (think along the lines of growth rate decline or churn rate turning negative.)
I'd also consider other seemingly innocuous or even "good causes" of this type of change in inbound links, such as disavowing links or asking for links to be removed, both of which would likely have a negative impact on growth rate and increase churn rate to the negative side, and would likely be "picked up" or "noticed" by Google over time rather than immediately.
3.) Template/Internal Structure Change: Was there any type of change along those lines that could be "making it's way through the system" and having a "slow impact" as more of the changes are processed and "understood as a whole relating to the site" over time?
[edited by: TheOptimizationIdiot at 8:37 pm (utc) on Mar 7, 2013]