Logging to a remote syslog server requires several steps. First of all, make sure there are no firewall rules blocking UDP/514 between the router and the syslog server.
Then remove the current logging setup:
"no logging #.#.#.#"
Finally, add the following:
"logging #.#.#.#"
"logging trap informational"
"logging source-interface Ethernet 0"
"logging facility local7"
Substitute "informational" for the severity level
Substitute "Ethernet 0" for the interface
Substitute "local7" for the facility
This had me puzzled for days, because IOS seems to need these config statements in a sequence.