Why was it easier to decode messages that you had several copies of?
Dooley says that simple substitution or transposition were used by both sides from 1914 to mid-1916--for radio, telegraph, and phone messages. Radio became more important in the summer of 1916, and then cryptanalysis became the name of the game for determining order of battle.[1]  Crystal set radio often required messages to be sent repeatedly due to signal attenuation, interference, operator error, etc.  But this is probably not what he was referring to.

Von Bernstorff was likely referring to the debacle of the Zimmermann telegram, where the same message was sent using two different encryption systems from Berlin to Mexico City.  It was a British intelligence coup.  Both cipher systems were weak, but the older one was almost completely broken.

The Germans did that because their embassy in Mexico City did not have their government's more modern cipher book.  Their people in Washington, D.C., fatefully relayed the Zimmermann telegram using an older cipher system.

Unsurprisingly, we have evidence that Von Bernstorff did employ one cipher which probably worked against the British, and that was the null cipher.
David Kahn says how Bernstorff used null ciphers in press cables to get past British collection.[2]

[1]  Dooley, John, F. (2016) Codes, Ciphers, and Spies: Tales of Military Intelligence in World War I (p. 49). New York, NY: Springer.

[2]  Kahn, David (1967) The Codebreakers (pp. 521 and 1063). New York, NY: The Macmillan Company.