Trouble triggering existing mechanical doorbell.

I have a Ring Video Doorbell Elite, which is powered over ethernet and connected to a mechanical chime via two wires. There is an odd issue that when the doorbell chimes, only half the mechanical chime goes off - ie the 'ding' without the 'dong'. When testing the chime separately the ding sounds when the circuit is closed, and the dong when it's opened again - so the push and release of a traditional button. It therefore seems like the Ring Doorbell is closing the circuit, but never opening it again - which seems like a bug? If I open up the doorbell and manually open the circuit by removing the 9v battery the dong does sound, so this seems to verify that. It also makes me worried that the battery will drain really quickly if the circuit is just left closed by the ring. I have tried using the digital setting to trigger the bell, and it doesn't seem to make any difference. Thanks for any advice.