As noted at the top of this page, delphiniums can be a challenge; not all grow as perennials. Many are short-lived plants. Knowing that, you could experiement: Cut them back as advised in Care above. Put them into a garage or basement and water them occasionally. Or, if you are in zone 7 or lower, lift them from the pot now and plant them (you could also plant the pot), then lift them in the spring and repot to see if they come back.
As noted at the top of this page, delphiniums can be a challenge; not all grow as perennials. Many are short-lived plants. Knowing that, you could experiement: Cut them back as advised in Care above. Put them into a garage or basement and water them occasionally. Or, if you are in zone 7 or lower, lift them from the pot now and plant them (you could also plant the pot), then lift them in the spring and repot to see if they come back.