Logging stands and Quarries are like any other collectable you use in crafting, as far as I know, as they are good for one use and unlike some materials they don't respawn. So once you find and claim a location that is all you can do with it and if you need more you have to locate other locations to fill the requisitions.
To use a logging stand or quarry, you are generally in the requisition table screen, which in Skyhold is in a building behind Cassandra and the fast travel marker(top left corner of courtyard). You will choose for instance upgrade courtyard and it will show you needing X number of logging stands, and Y number of Quarries and then you choose upgrade and it uses them up and you have to find more before you can do another.
If this is NOT what you are seeing, then reply back with maybe more explanation of what you are getting and we will try to help.