Well, I have a DSL hooked up at home, where I have flashfxp running virtually 24/7 for the last 6 months, only stopping to upgrade every other day.
I've yet to experience anything like what you experience, so I'm pretty sure it's not directly caused by the program. It might be indirectly affected by a poor configuration or some external element (firewall, routers, the servers you're using, the ISPs own ingenious ideas of a good setup), so it's pretty hard to pinpoint without any further info.