My intent was not related to a persistence issue itself, but rather that particular evar not having any value that persists. In the end, 'avg time' does not appear whenever the 'unspecified' value is shown for classifications or the underlining evar. 

Not sure about the technical reason, but I always find 'avg. time' to be zero for 'unspecified' values when using evars or classifications. I'm suspecting it has something to be with a value not persisting, and there is no second element to make that calculation. 

Something else to consider is the 'Internal URL Filters' that is set for each report suite. Keep in mind that MC processing rules is a waterfall process, and it would be best to put the 'Internal' channel towards the bottom. One of the rule parameters for MC processing rules is 'referrer matches URL...