iphone podcast app deletes played episodes even if "delete" option is off
I figured this out.  There's a global "Delete Played Episodes" option in the Settings app under Podcasts.  Rather than being a default setting, that is overridden by specific settings per podcast (as one would expect), this is a gobal override that renders totally ineffective any per-podcast settings.  With no indication anywhere inside the podcast player app that this is the case.  

If you're going to make it a global override, the least you can do is make the player UI gray-out the setting on the individual podcasts to inform the user that changing it there will have no effect.

This is clearly a bug but I doubt I'd get anyone at Apple to listen.