[Android Central Question]

I had hoped dropbox would be the solution, it works well from computers, but it seems their Android app doesn't handle slow, intermittent connections well: it restarts the transfer from the beginning, making large files impossible to upload.

[Rukbat]

You need an FTP app that handles restart. That way, it restarts the transfer at the point it ended when the connection was broken. But the server you're uploading to has to handle it too. There's no cloud backup service that I know of that does raw FTP transfers. They all suffer from the same problems with timed-out connections. (None of them handle restart in downloads either - download managers do - that's how they speed up downloads - but cloud backup servers ignore the request for a restart.)