This is an interesting dilemma. If the network isn't reliable, it seems that it would make sense to have a local server or programs running from the PC's that would talk to the remote server and keep a local log / copy of all the data. Running a "cloud" service presupposes a reliable network.
Getting a reliable network would seem to be the right answer but if that isn't possible, then you will have to live with some limitations and potential issues. It seems that maybe you need a dedicated PC that would initiate a connection to the server every 30 minutes or so and extract all of the updates since the last extract. It would need some sort of local program (always running!) that would be able to take some queries and display the data. That might be XAMPP with some local PHP and MYSQL but it could be some Basic or C or something else. Depending on the volume of transactions, you might not even need a sophisticated database in a backup scenario. You can probably deal with the security aspect but if someone steals the backup PC or turns it off or if the program crashes or there are any other problem with it then backup is out the window. You can use one of the remote control programs to manage it if you aren't nearby but once the network goes down, you're out of luck. In that case maybe it also needs a dial-up modem too. Maybe someone will come up with something really slick but it is a difficult set of limitations.