I would suggest starting but using something like Charles Proxey (or any other similar utility you trust) to identify what is being sent back and fourth from the client to the server. You may also want to log steps in you CFC's to a text file to see how far it's getting.
Most of the time when I have seen something like this in my own projects I find it's either network related or I have some funky setting I left in a CFC for testing I forgot to turn on or off.
For example: In one instance I was not able to get a CFC to respond on one system but the one next to it worked fine. I found out that one system ran to one switch and the other system to a second switch and the second switch was having problems and causing enough lag that the connection was timing out. It had nothing to do with my code at all.
Alternatley I often will block certain IP Address ranges in my code so that when in a development environment no system that is not on my Allow list can run certain CFC's. I once spent an hour troubleshooting code only to figure out that I had forgotten to add my new laptop to the allow list.
Might also want to verify there are no firewall issues blocking ports. Windows Firewall is a real bugger at times regarding this. I have seen it turn itself back on after updates.
And if you go through a Proxy server you will want to verify that the Proxy is not caching pages. Especially if you are using CF's Session State Management in any way. Set the proxy to not cache any pages from that particular site.
Regardless though it's best to see what's actually getting sent to and from the server first before trying to troubleshoot. So start with Charles or the Network Monitor if your using Flash Builder.