There is no appeal process per se, but you can appeal the late filing penalties if you are assessed. You could perhaps argue that the letter was in fact postmarked on or before March 15, and ask them to produce the envelope. March 15 was a Friday, so they would not have received till March 18th or 19th at the earliest.
One thing we had happen here in my office is that we frankly blew an extension for a Mass Corporation with a 12/31 year end and the extension was due 3-15. We went on line and requested an extension for the year 1/31 and the extension was due 4-15. This allowed us to pay the excise tax and the corporation was on extension, albeit the wrong one. We then filed the tax return 6 months later. There was some nasty gram that said "You filed an extension for the wrong period and we are assessing penalties." The penalties were like $10. Nothing.
As I am typing this, I came up with a completely different stratregy. If you try to e-file an extension on time, and you cannot make it work, you normally get a 5 day grace period to submit on paper.
You could argue that you tried to e-file on line on March 15 and were unsuccessful and wish to use the 5 day grace period to file on paper what
was previously rejected online. (Obviously, you don't have screen shots), but I have found this goes pretty well.
So, in summary, there is no appeal on hardship but you might get reinstated based on postmark or e-file rejection.
No, I don't have a cite, but every e-file department by definition has to have a rule that says "If you try to e-file on the last day, and it's rejected, we allow you a grace period to correct the deficiency on paper". I called the NY e-file help desk at(NNN) NNN-NNNNand they confirmed this, and no,. they did not know a specific cite. You might be able to get them to rectify this.