Getting timed out of SSH and SFTP when transferring several files

Question

To work remotely, I use SSH to connect to a workstation at my university to run programs and I use the application CyberDuck to perform SFTP to transfer files. What invariably happens is that when I transfer several files (about 20MB, but lots of little files) the transfer process will eventually fail saying that it has failed to connect (to the server I was just connected to). After this, moving over to SSH in terminal, it doesn't work and tells me that port 22 is now broken. When I try to ping the server IP, I get 100% packet loss.

I have tried to investigate the possibility that my ISP is responsible. They (Bell) have a GUI for the modem where I can select "port forwarding" and I tried to ensure that ports 20, 21, and 22 were kept open. This, however, has not solved the problem.

I think that the problem is on my end because (a) if I use a different WIFI the SSH will work again, and (b) it seems like after this happens my computer cannot SSH into anything. In fact, when I use the Network Utility app on mac the port scan is not returning any information on ports 20, 21, and 22.

When I check my port 22 on canyouseeme.org, I get:

Error: I could not see your service on (my IP ADDRESS) on port (22) Reason: Connection refused

This has been an ongoing issue for me that I have never got around to solving because I often would just wait for it to resolve itself (after a few hours it usually works again -- but will fail again if I try an 'ambitious' sequence of file transferring) and because I often work at school - where, even if I'm not at the workstation itself (I am in the same room or at least building, though), these SSH and SFTP protocols still work without fail. I really would like to solve this once and for all and would sincerely and gratefully appreciate any insights.