@Rich Matheisen
Nope, I'm not using the Invoke-Command cmdlet. I'm using the simple string "Get-ADReplicationFailure -target 'mydomain' -scope Domain -Verbose" alone and it returns information about almost all of the DCs in both my sites except one. And if I run the string "Get-ADReplicationFailure dc_name" on the very DC that is not returning information, I don't get any output there as well...
I followed the suggestion you gave me in your reply 8 days ago: "If "Get-ADReplicationFailure" is the only thing in the script, try adding the "-Verbose" switch to it."
Do you want me to use the Invoke-Command cmdlet instead?