We've constantly having problems on construction sites where contractors don't have internet connection to "transfer" the latest drawings through the BIM 360 Desktop Connector to resolve on-site issues for the day. Especially unplanned items that creeps up.
There is also the issue that they need to open/ sync multiple documents to ensure the files "transfer" before the required date - especially with the 72 hour (can't remember exact time length) sync enabled.
I would propose that the desktop connector gets something like Office 365 Files on Demand or Keep Synced option where you can choose which folder you want perma-synced with your PC, so every time you connect with the internet it will download and keep up to date the drawings with the latest information.
The Files on Demand is what is currently used where it will "transfer" the drawings once opened for a period of time.
This is required for teams that uses laptops on-site.