Student: Sorry I couldn't do my homework.
Teacher: You could ask your parents to help you.
Is it possible to use the teacher's sentence to make or refer to a suggestion in the past? Or we have to use could + have + past participle?
The dialogue is correct if the teacher means, "When[ever] you can't do your homework, you could ask your parents to help you." And this is just as likely.
The teacher's line is only incorrect if you assume s/he means "could have asked".
But, no, you can't use "could ask" to mean "could have asked".