At the risk of sounding sarcastic (which I'm not meaning to be at all), which variety of Agapanthus you buy is critical. Many of them are not fully hardy outside and need to be overwintered in a greenhouse or similar. The most reliably hardy varieties in the ground are the Headbourne hybrids, but even those, if they're in a pot, will need to be put somewhere sheltered and preferably sunny, and where they don't get too wet over winter, particularly where you live. Wrapping the pot in bubblewrap also helps to insulate the bulbs.

Raising the pot onto pot feet helps too.

Thanks - Into greenhouse on feet