Why can't we drink wine that was made by a non-Jew but was made from beginning to end by machine? Needless to say that according to the Gemara that it is only yayin nesech if the non Jew makes an actual libation with it. Even if you want to call it yayin stam, according to the Gemara it's only yayin stam if the non Jew touches it after all the wine has been stored in the barrel to ferment, since before it is put in the barrel it is unfit to drink or be used for a libation.
Probably because of what the Shulchan Aruch, Yoreh De'ah says in סימן קכה - דין יין הבא מכח עובד כוכבים וכח כחו
ב: כֹּחַ כֹּחוֹ כְּכֹחוֹ דָּמִי. וְאִם הוּא כֹּחַ כֹּחַ כֹּחוֹ, כְּגוֹן קוֹרַת הַגַּת שֶׁגִּלְגְּלָהּ עוֹבֵד כּוֹכָבִים, שֶׁיֵּשׁ שָׁם ג' כֹּחוֹת: הַדַּפִּין וְהַגַּלְגַּל וְהַקּוֹרָה, (ד) בְּדִיעֲבַד מֻתָּר אֲפִלּוּ בִּשְׁתִיָּה.
And the Be'er Heitev adds:
באר היטב (ד) בדיעבד. אבל לכתחלה אסור אפילו בעשרה כחות ויותר כן משמע בטור ופוסקים:
That while - after the fact - a non-Jews triple-indirect actions may be allowed, one preferably doesn't have a non-Jew involved in making wine even if his actions are 10-times removed.
So, even having a non-Jew press a button to start a machine would be unacceptable.
Rabbi Frand has a tape where he says he likes to drink grape juice all the time, and wondered about this -- it would be a lot cheaper if he could buy regular (non-kosher) grape juice. He was told even with today's fancy-schmancy machinery, there's a human hand someplace in the factory unclogging a filter or the like every so often.