Based on the example you provided, it looks like you're using a tab delimited file. What happens if you use the Schema.ini file without including the TextDelimiter line?
Not sure why it worked, but your suggestion seems to have fixed the problem. For a little background, I came across the option for "TextDelimiter=" in a Tableau forum comment and figured I should include it in my own schema.ini file. But removing it seems to have done the trick. I would have thought Tableau would simply ignore an option that wasn't valid, but apparently not. Very strange.
I'll keep monitoring to see if the problem returns, but for the time being, we can consider this issue solved.