During

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late Middle English: present participle of the obsolete verb dure ‘last, endure, extend’, via Old French from Latin durare ‘to last’ (see duration).

wiktionary

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From Middle English during, durynge, durinde, durand, durende, present participle of duren(“to last”), equivalent to dure +‎ -ing. Compare Dutch gedurende(“during”). More at dure.

etymonline

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during (prep.)

"in the time of, in the course of, throughout the continuance of," late 14c., duryng (earlier durand, mid-14c.), present participle of the long-obsolete verb duren "to last, endure, continue, be or exist" (mid-13c.), which is from Old French durer, from Latin durare "to harden," from durus "hard" (from PIE root *deru- "be firm, solid, steadfast"). During the day is "while the day endures," and the prepositional usage is a transference into English of a Latin ablative absolute (compare durante bello "during (literally 'enduring') the war").