I'm not familiar with Website Tonight. Analog and Report Magic process whatever log files you point them at. If you have historic log files for processing you can change your Analog configuration to look at those files. See
Most web sites these days don't store log file for more than a week or two, so that may be as far back as you can get with log files alone. If Website Tonight deletes only log files you can still use analog's cache mechanism
to keep statistics from old log files around for a longer time. Alternately, you can configure Report Magic to write statistics our for daily or weekly snapshots to date-named folders
in the output file setting to keep historic records.
If you don't have access to the configuration files you'll need to talk to your hosting company about making these changes.