you may try again, and note the time of the initial connection, and the time you observe the connection drops.
Then check logs to see if there is any indication of who dropped the connection (remote or local)...
You mentioned 3 machines - hopefully I am correct in interpreting your post as such. So if it is your machine (1) that drops the connection to (2) after you have started a transfer between (2) and (3), I believe that transfer will also be severed. If you run the scp on (2) in the background, however, it should outlive your shell, I think. Just make this
scp myfile.txt otheruser@otherserver:/path/to/file
scp myfile.txt otheruser@otherserver:/path/to/file &
and you should be able to verify later whether the transfer was successful; you could even redirect output from scp to a local logfile somewhere on (2) where it is running and then it would leave you a trace.
If (1) and (2) are close to each other (like in the same office) you should work on resolving that network issue - some kind of timeout limit? Bad cables? Intermittent wireless access? A failing router or switch?
May want to move post to Networking.