Uploading files to cloud backup service is causing us to lose connectivity

We've got a business account that seems to be getting flagged by your network causing our modem to lose connectivity.   We're a cafe with customers using our wifi and our point of sale system conducting transactions over the network.  Tonight we tried to upload a couple of thousand small (<= 8MB) files to Amazon S3 for backup purposes and our modem keeps losing connectivity every few hundred files.  This causes our customers to get dropped and the business to come to a halt.  We should NOT have to be throttled or disconnected for ONE user uploading a bunch of files which are queued to upload 10 at a time.  Resetting the modem brings back connectivity but once the upload starts up again, it goes down.  It would be less of an issue if it only happened to the uploading user but having everybody in the cafe lose connectivity is stupid.