Postgres auto analyze performance
I think your best option is to use your favorite OS scheduling tool to run ANALYZE &lt;table&gt; explicitly and pre-emptively at the time of your choosing, say at 3 a.m.

PostgreSQL's autovacuum and autoanalyze are activity-counter driven.  This has the unfortunate effect that the time when the activity counters cross the thresholds is mostly likely to be exactly when the database is most active, which is when you least want those maintenance tasks to run.  By running the task preemptively during a off-peak time you will reset the activity counters, so that the auto-versions rarely will find work to do.  But in case of something going wrong, they are still there to save your bacon.


  Will the query planner eventually suffer from not having auto analyze running on a table that never gets updates or deletes?


This can't be answered with the information you provide.  If that table gets nothing but single-row lookups via a unique index, for example, out-of-date statistics are unlikely to be a problem.  If it gets complicated analytics queries, it is likely to be much more of a problem.