How do I keep podcasts I've downloaded on my iPhone after syncing with iTunes?

I like to download entire series or sometimes save shows on my Podcast app for binge listening or reviewing later.

However, if I download (for example) twenty episodes of a particular podcast, and then sync my iPhone, it deletes all the podcasts I've downloaded.

Is there a way to mark a podcast to stay on my iPhone until I mark it as listened to, or otherwise note that I'm done with it?

It seems to be a bit of a pain that you're given the option to download, but simply syncing for some reason deletes all the shows.

Any help is appreciated!