I've only encountered this bug on Nessus so perhaps it also happens on other Destinations.
Basically, after killing the 1st small Servitor, no other Servitors will spawn. So the main Servitors shields stay up, preventing any damage from being done, halting progress on the Event. All you can do is wait out the Event timer.
To my surprise I found a [url=https://www.reddit.com/r/DestinyTheGame/comments/keq5x9/ether_resupply_in_nessus_is_bugged/?sort=confidence]Reddit post[/url] from three years ago, talking about this bug, with comments as recent as 1 month ago still commenting on it.
Has anyone else encountered this glitch?