I think we’ve heard this in much simpler terms … something like “he who hesitates is lost” or words to that effect.

I prefer this more elegant phrasing which dramatizes both the elation and exhaustion that arrives just as we’re nearing the finish line. We’re tired of the race … or just plain tired … and figure we’re almost there so, hey, let’s catch our breath.
Sports is a metaphorical gold mine for this syndrome. How many likely winners failed in the last minutes, ran out of steam … and lost a game or race they should have won?
Winston Churchill added this riff at the end of all of his wartime correspondence during World War II:

KBO

Keep Buggering On.
Still good advice, huh?
Grab the gold ring first.
Then … and only then … sit down and enjoy the victory.