It's hard to tell what is happening here. Is it maybe possible to get access to your Piwik instance and to your database maybe?

I don't think that will be possible since the install is within our Internal Network. Basically for one Site ID when I pull a date range of anything of 4/04 or prior to current date, the resulting report drops the data for one date (4/08). For example if I put in date range of 4/01 - 4/17 the results do not include 4/08. If I put in date range of 4/05 -4/17, results do include data for 4/08.

This also happens if I use selection of "month" April or "year" 2016, the results to do not include data for 4/08. However, the data is in the database when I direct query such as this:

SELECT    idaction_name as id, 
          COUNT(idlink_va) as views,
          COUNT(DISTINCT idvisitor) as visits,
          COUNT(IF(idaction_url_ref=0, 1, null)) as entry,
          piwik_log_action.name as page
          FROM piwik_log_link_visit_action, piwik_log_action
          WHERE piwik_log_link_visit_action.idsite= 2
          AND piwik_log_link_visit_action.idaction_name = piwik_log_action.idaction
          AND server_time >= '2016-04-07'
          AND server_time <= '2016-04-10'
          GROUP BY idaction_name
          ORDER BY piwik_log_action.name

Question: is there some kind of reporting process that we can rerun to update the data?

Yes, this should help I presume: http://piwik.org/faq/how-to/faq_155/

To be clear, marking the date as invalid will not remove data for that date from the database? The way it reads it will "reprocess" the reporting for that date...

It will not delete any logs. It will only invalidate existing report archives. So it is possible to regenerate the archives afterwards

Following the examples in the article, I ran this command in the Console. Does using "Dry Run" mean it didn't actually run or is just showing me the accompanying SQL queries and it did in fact invalidate the dates?

*php ./console core:invalidate-report-data --dates=2016-04-04,2
016-04-08 --sites=2 --dry-run
*

``d:\wamp\www\piwik>php ./console core:invalidate-report-data --dates=2016-04-04,2
016-04-08 --sites=2 --dry-run

Invalidating day periods in 2016-04-04,2016-04-08 [segment = ]...
[Dry-run] invalidating archives for site = [ 2 ], dates = [ 2016-04-04, 2016-04-
05, 2016-04-06, 2016-04-07, 2016-04-08 ], period = [ day ], segment = [  ], casc
ade = [ 0 ]
Invalidating week periods in 2016-04-04,2016-04-08 [segment = ]...
[Dry-run] invalidating archives for site = [ 2 ], dates = [ 2016-04-04 ], period
= [ week ], segment = [  ], cascade = [ 0 ]
Invalidating month periods in 2016-04-04,2016-04-08 [segment = ]...
[Dry-run] invalidating archives for site = [ 2 ], dates = [ 2016-04-01 ], period
= [ month ], segment = [  ], cascade = [ 0 ]
Invalidating year periods in 2016-04-04,2016-04-08 [segment = ]...
[Dry-run] invalidating archives for site = [ 2 ], dates = [ 2016-01-01 ], period
= [ year ], segment = [  ], cascade = [ 0 ]

dry run does not actually execute the queries

Thank you for your advice to invalidate the problem dates and regenerate the reports, it appears to have worked and fixed the reported issue.

Awesome, thx for letting us know.