"Running down" can mean losing power or energy, as with a battery or clock. It can also mean chasing and catching someone or something. It may also mean criticizing someone, or listing items quickly.
all my life i have lived and behaved very much like the sandpiper just running down the edges of different countries and continents, looking for something. Elizabeth Bishop
Two things are bad for the heart - running up stairs and running down people. Bernard Baruch
He had been full of the idea so long, dreamed it right through to the end, waited with his teeth set, so to speak, at an inconceivable pitch of intensity. Now, in the reaction, he was running down like an overwound clock. F. Scott Fitzgerald
If you see somebody running down the street naked every single day, you stop looking up. Stevie Nicks
The tears running down your face do not blind you. Togolese Proverb
Virtue: climbing a hill; vice: running down. Chinese Proverb