As i know theres no a rebuild option for the destroyed building of the map. untill is destroied, it will stay destroied untill the server restart.
the nearest thing is to achieve something similar trough a bit of scripting and mission editor trigger.
using MIST Mapobjs dead zones https://wiki.hoggitworld.com/view/MIST_Mapobjs_dead_zones you can declare as you say a trigger zone aruond a single map object (or more), for example a bridge, or you can draw a trigger zone around a gruop of map objects, for example an entire village.
you can creata a trigger zone around a bridge called "bridge1" and then declare
mist.flagFunc.mapobjs_dead_zones{
zones = {'bridge1'},
flag = 1050,
req_num = 1
}
that means when the req number of structure (1) in the zones called "bridge1" got destroyed, the script trigger on the flag 1050.
in mission editor, you can set one at once with conditions "flag 1050 true" and as action you can for example make the spawn of an unit in the border of map, you use that unit as "persistent" flag.
if there no that unit, it means the bridge is alive
if theres that unit, it means the bridge got destroied.
then, you can associate the presence of that unit to a scenery destroy trigger in mission editor, and make the bridge explode itself one second after the start of the new mission, so you can have a kind of persistence about the status of mapobject.
when someone complete the repair mission, you remove the unit created by this metod, without the unit at restart, the bridge will not be destroyed and come back alive.
theres no way to rebuild it in "real time" as i know,, you have to workaround trough metod like that.
theres surely different way to do that with moose, mist, and mission desanitizaiotn by the way ,and the one i suggest should be on of more, not the best not the worst.
if you are familiar with mission desanitizaion and local save of file trough lua script you can achieve the same thing without involving mission editor trigger.
Also, with a bit of fantasy, you can achieve similar result without scripting but using the "bomb in zone" trigger
kira_mikamy's post in Need Mist help to remove spawned ai. was marked as the answer