Gary,
Thanks for the sample! I was able to figure out what was going on, the problem isn't acutally in the Update instead it's when the original feature is added to the EditLayer in your form load. In the code you provided you were adding the feature with the following line of code in the form load.
dragInteractiveOverlay.EditShapesLayer.InternalFeatures.Add(LineFeature);
Since this feature was added outside of the EditTools API the EditTools didn't register the ID and so when the Update was called in your click event the feature wasn't found and the update failed.
In order to resolve this instead of using the Add off of the InternalFeatures collection you should use the EditTools API to add your feature like the code below in the form load, this way the Adding and Updating will be done by the same API's and be consistent.
dragInteractiveOverlay.EditShapesLayer.Open();
dragInteractiveOverlay.EditShapesLayer.EditTools.BeginTransaction();
dragInteractiveOverlay.EditShapesLayer.EditTools.Add(LineFeature);
dragInteractiveOverlay.EditShapesLayer.EditTools.CommitTransaction();
dragInteractiveOverlay.EditShapesLayer.Close();
As a rule of thumb I would never use the InternalFeatures collection i and always use the EditTools when the features have the possiblity of changing. The InternalFeatures collection is a quick and dirty way to access the features and hasn't been fully tested for editing scenarios.
One other helpfull tidbit of information when using the EditTools is that you can actually check the results of the transaction. Many people don't know this but it can be very helpfull in debugging issues when editing featurs. To see the results of the transaction you just interogate the TransactionResult object returned from the CommitTransaction method.
TransactionResult tr = dragInteractiveOverlay.EditShapesLayer.EditTools.CommitTransaction();
Thanks for reporting the issue and let us know if you have any additional questions.
Thanks!