In addition to what others have said, there's always the possibility of Windows-based hosting to allow mIRC to run on a remote server.
Or, if the information the bot takes doesn't need to be accessible at any time (eg. if you're the only one who uses the information it logs) then you could use regular eggdrop logging to keep a continuous record and then sync the eggdrop's logs with your bot each time you reconnect.
