The closest I can come to an official ruling on this is to actually fast-forward to 3.5e, so take this with a grain of salt.
Let's compare the "one attack" duration to a "touch spell". In the case of a touch spell, the PHB explicitly states a touch spell can be held indefinitely so long as you don't discharge the spell.
I would treat this spell the same. It won't discharge until there is an attack.
From a more storytelling side of things, let's talk practicality. Your weapon has 5 additional feet of reach. The spell explicitly says your weapon stretches, so we can assume a physical change in shape. So let's say you have a magic sword that just extended 5 feet (you took your normal reach, added 5 feet to it, I believe it's safe to say the weapon itself grew 5 feet). Are you going to carry around a 7 to 8 foot sword all day?
That actually gets me thinking. You have a 7 foot sword. It accidentally drags on the ground. Does that discharge the spell? Does it have to be an intentional attack? Could you accidentally discharge your spell. Like when you rub socks on a carpet, get all staticked, then try to shock your friends. Chances are you discharge yourself unintentionally before you get remotely close to your prey.
I officially have more questions than answers.