Assuming your Amazon EC2 instance is running Linux (and the very likely case that you are using SSH-2, not 1), the following should work pretty handily:
Remote into your EC2 instance.
ssh -i <YOUR_PRIVATE_KEY_FILE>.pem <INTERNET_ADDRESS_OF_YOUR_INSTANCE>
Add a "client-alive" directive to the instance's SSH-server configuration file.
echo 'ClientAliveInterval 60' | sudo tee --append /etc/ssh/sshd_config
Restart or reload the SSH server, for it to recognize the configuration change.
The command for that on Ubuntu Linux would be..
sudo service ssh restart
On any other Linux, though, the following is probably correct..
sudo service sshd restart
Disconnect.
logout
The next time you SSH into that EC2 instance, those super-annoying frequent connection freezes/timeouts/drops should hopefully be gone.
This is also helps with Google Compute Engine instances, which come with similarly annoying default settings.
Warning: Do note that TCPKeepAlive settings (which also exist) are subtly, yet distinctly different from the ClientAlive settings that I propose above, and that changing TCPKeepAlive settings from the default may actually hurt your situation rather than help.
More info here: http://man.openbsd.org/?query=sshd_config