Reuven Kimelman has an article in the Seforim blog exploring the nation of Amalek as they appear throughout Tanach. From his close analysis, he comes to some novel conclusions which I would summarize as follows:
- The mitzva to remember Amalek is presented in the Chumash as moral rather than ethnic in nature
- The mitzva to blot out the nation of Amalek is limited to a future time, specifically Shaul Hamelech's campaign(in which he spares Agag and much of the booty and is told the kingship will be given to another)
This latter point is based on the observation that Amalek appears many times in Nach, but that only during Shaul's campaign does the scripture relate to them as meriting annihilation.
As such, the command in Dvarim 25:19 is read not as a mitzva for the generations, but rather as a reason for the mitzva of remembering Amalek and the promise of a future effort to destroy Amalek, limited to a particular time period.
וְהָיָה בְּהָנִיחַ ה' אֱלֹהֶיךָ לְךָ מִכָּל-אֹיְבֶיךָ מִסָּבִיב, בָּאָרֶץ אֲשֶׁר ה' אֱלֹהֶיךָ נֹתֵן לְךָ נַחֲלָה לְרִשְׁתָּהּ – תִּמְחֶה אֶת-זֵכֶר עֲמָלֵק, מִתַּחַת הַשָּׁמָיִם; לֹא תִּשְׁכָּח.
This brings us back to a previous post on this blog about the relationship between the two mitzvot, to remember and to destroy Amalek. Kimelman's approach lines up with that of the Minchat Chinuch, that we have two independent mitzvot, differing in the historical period during which they apply, as well as in who is obligated.