Just a follow up.

I still don't know what caused some of my linked servers to lock and not others, but I am back up and running.

The only suggestion I had gotten from anyone that I had not tried was to reboot the server, immediately start a trace and determine at what point the linked servers stopped responding.

I did this, but while previous server reboots had resulted in temporary restoration of linked server activity followed by them failing to respond within half an hour of reboot, this time that didn't happen.

All the linked server connections came back online after the reboot, and even though I had my trace running for hours hoping to catch the suspect query that killed them, nothing did.

So, five days on, we are working, and hopefully will continue.