I like the cool helicopter avatar you chose to use in the Intel communities.
You might be running into a situation where the signal from some switches or on some cables doesn't quite meet Ethernet specs. That might explain why you do not have the drops connecting to some switches, but you do have an issue when connecting to other switches.
Watch for the next software release, which I expect will be available soon. By soon I mean you will find counting the time until the next software release in days rather than weeks. Depending on the exact cause of your drops, a driver update may or may not help, but I think the next driver has a good chance of helping you.
The other thing is to make sure your computer has the latest updates to BIOS and/or firmware from Lenovo. I have not checked to see if the X220 has updates available, but as a general rule, these updates can affect your built-in network connection.
I am looking forward to hearing about your results from any updates you make.
I hope this helps.