I believe you are talking about FMS AWS instance and you may be using a centos 4.0.2 instance AMI or lower?
Well ... earlier, options for stopping a centos AWS image was not available, but recently they are there in place, so I suppose if you use a new centos 4.5.1 AMI then probably you can start stop the aws instance on yuor will. Give ut a shot and let me know.
I again cross-checked and found that you were right, start and stop is not supported there .... an alternative method is to take a snapshots of the runinng instnace and terminate that instance after that, later you can use your snapshot to attach to the EBS volume to run your system again. You may need to use the Elastic IP address, because you wont like your users to update each time you terminate the old instance, and create new instance from snapshot. I have never used it in this way, but this is one of the approach.
I am afraid but the FMS offering is still based on local instance store and is not EBS backed, so you can only Terminate/Reboot your instance. So you wont be able to Stop/Start it. However by using other AWS features, I think you may be able to reuse your configuration.
1. Try creating a volume and saving all your configurations and files under it. You can attach this Volume to your in stance when you create one.
2. In order to use the same IP on client side, get hold of an 'Elastic IP' and associate to your instance as desired.
3. You don't have to keep a volume ready at all times. Please check how 'Snapshots' work. I believe you can take a snapshot of your Volume and then later create an actual Volume from it.