Before you throw your PS Vita against the wall, run this checklist:

Your Vita’s IP address changes every time you reconnect to Wi-Fi (unless you set a static lease).

Troubleshooting VitaShell FTP: Why It Fails and How to Fix It

Start with the simplest fix: cycle the Vita’s flight mode, re-enter the IP manually, and limit your FTP client to one connection. If you are still stuck after 30 minutes, abandon FTP and use USB mode. It is less glamorous, but it will transfer your ROMs without the headache.