I would say it would most likely be a router or firewall issue, but there is a history with Filezilla and this problem before. Are you a firefox user, maybe try their ftp plug-in, and see if you can connect to your ps3 with that.
If not have you thought about using a dynamic IP? and setting the ports on your router, or connecting direct, not though a router? Also with in FileZilla under settings have a play with the Timeout settings, maybe change that to 0, and the Max retries to 5. Or use Blackbox or deanrr's