I just changed the “access All” to “no” for the Beaverkill Covered Bridge because it is closed to all users during reconstruction. After saving the changes, OSRM still routes across this bridge. Is this a just a time lag or is OSRM not designed to avoid closed roads?
It’s time lag, OSRM udates less frequently than Mapnik (=main osm.org layer).
P.S.:Also, you may change the highway tag to highway=construction for the time of reconstruction. 
What is the estimated duration of the works?
Some unknown number of months. They boarded up the ends early this summer and have barely worked on it.
It seems that the update process for the routing database by OSRM has stopped for unpredictable time … there are already issues on github.com about that.
See the website settings on http://osrm.at to see the date of last database update (right bottom of screen)… for now it is “n/a” … 