Well it depends on the appliance I suppose.
logmon has the ability to parse the output of a script you supply. Possibly you could have a script that retrieved new log entries from the appliance and directed those entries to stdout. Then use logmon to run that script and filter the output.
Does the appliance support syslog? UIM has a syslog listener that could possibly be set up as a target.
How about SNMP? maybe you don't need the logs if you can directly test whatever would be recorded in the logs?
-Garin