It helps us a lot if you give the context of your quote. If you add several sentences before that sentence, and perhaps after it, that saves us from having to look up your quote to find that information. Thank you for giving the title of the book, which made it a little easier. As you can probably guess, it is very old English, so it certainly isn't natural, modern language. That is partly why it isn't obvious to a 'normal' speaker what the meaning is. In your quote 'ill' means 'badly'. The quote is referring to coughing. So - it means that she coughs at bad times. So - perhaps she coughs when other people are talking, rather than trying to wait, and cough at a quiet time.