If you are able to follow the GPL terms, your distribution of binaries of GPL software is non-infringing. But as soon as you can't follow all of your obligations under the GPL terms, you are back to "All Rights Reserved" and none of the GPL terms apply to you any longer. At that moment, you are infringing.
If you do not have the complete and corresponding source code on hand for the three years during which you are obligated to fulfill a request, and have to recover them in some way that takes a significant amount of time, that is what the court would see as a failure of due diligence and you are infringing at that time. If there is any "reasonable time", it is only the time necessary to respond with a file that you already have on hand because you have pursued your due diligence in maintaining it. Due diligence is something you are expected to take care of before being sued. To the extent that you take care of it after being sued, that is a remedy. You can still have damages for the period of infringement before your remedy. So, if you fail to provide source code within just a few days, a lawsuit is filed, and you then manage to come up with a bit-perfect binary match (and good luck with _that_), you potentially have some infringing time for which damages can be assessed by the court. In practice you have that nice Bradley Kuhn who is more lenient than any court (I am speaking from experience). But he doesn't have to be. Thanks Bruce -- Sent from my Android phone with K-9 Mail. Please excuse my brevity.
