Here's some additional info culled from a log file:

2014-01-29 14:48:14.02 spid22s Informational: Full-text Full population initialized for table or indexed view '[MyDB].

.[FtsTest]' (table or indexed view ID '725121874', database ID '5'). Population sub-tasks: 4.

2014-01-29 14:48:16.05 spid40s Error '0x80004005' occurred during full-text index population for table or indexed view '[MyDB].

.[FtsTest]' (table or indexed view ID '725121874', database ID '5'), full-text key value '1000'. Attempt will be made to reindex it.

2014-01-29 14:48:16.05 spid40s Error '0x80004005' occurred during full-text index population for table or indexed view '[MyDB].

.[FtsTest]' (table or indexed view ID '725121874', database ID '5'), full-text key value '1001'. Attempt will be made to reindex it.

2014-01-29 14:48:16.05 spid40s Error '0x80004005' occurred during full-text index population for table or indexed view '[MyDB].

.[FtsTest]' (table or indexed view ID '725121874', database ID '5'), full-text key value '1002'. Attempt will be made to reindex it.

2014-01-29 14:48:16.50 spid87 Informational: Full-text Full population completed for table or indexed view '[MyDB].

.[FtsTest]' (table or indexed view ID '725121874', database ID '5'). Number of documents processed: 3. Number of documents failed: 3. Number of documents that will be retried: 3.