Q: iPhone 4S lock screen automatic disable 3G/EDGE

Thats because iphones arent serious business tools. There is a reason why apple is called the "fruit" company.

Activating the lock screen does not cause the cellular data connection to drop, it simply causes the device to go to sleep.  Any apps open are put into suspend mode.  If the app is actively doing something, it may complete depending on how the app is coded.

As for being able to ping the IP with the device in sleep mode, there's really no reason to expect a device in sleep mode to respond to pings.

As for the actual issue, if push email is configured correctly on the server and on the device, it does work.

Is the email account in question a work email? Gmail? iCloud? or?

As for being able to ping the IP with the device in sleep mode, there's really no reason to expect a device in sleep mode to respond to pings.

What about VPN connections. When the device is in sleep mode they will disconnect and you have to manually reinitiate the connection. So yes, I would expect the device to respond to keep alive pings from the VPN server.

If there is a VPN client/app running on the device and it's coded properly, the connection would stay active.

However, that's not the scenario that was described.

There is no reason for an iDevice to simply respond to a ping when in sleep mode by default.

If the intent is to test whether the data connection stays alive in sleep mode, install a streaming audio app like Pandora, DI.fm, or similar.  Start the audio streaming.  Then put the device to sleep.

If it continues streaming, then the issue is not with the device shutting down the data connection in sleep mode.

Has the simple solution to the original problem of deleting and re-adding the Exchange account even been attempted?

I'm referring to the built in VPN client, it terminates connection when the device goes to sleep.