In this instance, the Storm Trooper unit leader (who is holding an an objective) is the only model visible to the Droideka. As they can only kill what they can see, and the unit leader must be the last to die in a unit, if the Droideka successfully kill a model, when the unit leader is moved, does the objective move with it or does it get dropped when the unit leader moves?

Page 52 of the RRG "Objective Tokens":

"If a player’s unit leader with a claimed objective token becomes panicked or is defeated, before they remove or move the unit leader, that player flips the objective token to its unclaimed side and places it back onto the battlefield in the same position and in base contact with the unit leader. The objective token remains on the battlefield where it was placed and can be claimed again as normal."

Since the unit leader is defeated, then the objective token is left behind on the battlefield.

Edit: Also, page 31 "Defeated"

"If a player’s unit leader with a claimed objective token is defeated, before they remove or move the unit leader, that player flips the objective token to its unclaimed side and places it back onto the battlefield in the same position and in base contact with the unit leader. The objective token remains on the battlefield where it was placed and can be claimed again as normal."

Yeah I read those last night, but somehow missed this bullet on page 31:

"In the rare situation in which a unit leader is defeated and
there are still minis in that unit, the player who controls that
unit must immediately choose another mini in that unit to
become the unit leader—the player replaces the chosen mini
with the unit leader mini."

Thanks for the help!