You are kidding about this, aren't you?
Let me get the facts straight:
- you have "mission critical files", and the network you're transferring them over is so incredibly badly managed that it doesn't support reliable data transfer
- you want a technical workaround for this brokenness.
If this is the case, you don't have a technical problem on your hands; you have a political one.
"Mission critical" has a meaning: it means critical to the success of the operation. I.e. without these files, your operation or someone else's operation will fail.
If your management believes that your files are "mission critical", and you're facing a problem of this sort, you need to document the difficulties you're having, along with measurements to support your claims and then make a clear statement that as long as your network path is completely broken, you are absolving yourself of responsiblility for the correct transmission of these files.
If your management doesn't do anything about this, then the files are not "mission critical".