When autovacuum is off, the statistics in pg_stat_sys_tables for shared
catalogs (e.g., pg_authid, pg_database) never update. So seq_scan
doesn't update when you read the table, last_analyze doesn't update when
you run analyze, etc.
But when you shut down the server and restart it with autovacuum on, the
updated statistics magically appear right away. So seq_scan is updated
with the number of reads you did before the shutdown, last_analyze
updates with the time of the analyze you did before the shutdown, etc.
So the data is saved, just not propagated to the view properly.
I can reproduce this back to 9.3, but not 9.2. Any ideas?