First of all, I am no network expert. All of what I am saying here is what my brain came up with after listening and reading a bit.
When I want to run multiple toons doing some trade runs or something, I seem to get more disconnects entering stations or gating. It seems like most disconnects may be associated with loss of UDP protocol packets somewhere in the chain between the client and the server (potentially somewhere within the Internet as well). I thought about it a little and wondered whether there is anything on my end (client) that I can do to reduce the occurrences. On my PC, Windows has a single buffer receiving the UDP packets and I thought that multiple instances of the client would be trying to receive multiple packets pretty much all at the same time. If this buffer were small, the buffer may overflow from time to time and therefore generate some packet loss on my PC. So I decided to see what I could do (raise the size of the buffer). I went into Control Panel - Devices - Network Adapter - Properties - Advanced - Receive Buffers and then changed the size from 1024 to 2048. So far, I have not had any disconnects. I expect the value of the Receive Buffers on many PCs will be different depending on the resources available.
Remember that this is totally just what my brain came up with based on all the information that I have heard. It may or may not resolve some of your issues.