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The data is stored in the logger that you plugged into your console, not the console itself. Whether you will lose data will depend on if the time period that it was offline exceeded the storage in the logger. This is a function of the "archive interval". Mine is set for 15 minutes.
I have a plug-in for the Weatherlink Software Program that I can upload my Wunderground data that was missed due to a power failure. I have used that successfully. I am not sure about the mechanics on how (or if) any archived data is uploaded to Weatherlink.com. Since there is no graphing on Weatherlink.com, it probably gets the history data stored from the logger. Anyone who knows for sure is free to comment or expand on this.
Greg H.