Dustin,
By default the Advantage client will cache all connection (6000 class) errors. This was done so applications that made multiple connections would not waste a lot of time retrying connections. The default behavior can be changed by adding RETRY_ADS_CONNECTS=1 under the [SETTINGS] heading in the client side ADS.INI file.
This will force the client to retry the connection even if a connection error was received.
Here is a link to the help file that explains the various ADS.INI settings: http://devzone.advantagedatabase.com/dz/webhelp/Advantage11.1/index.html?master_ads_ini_file_support.htm
Chris