Exercise 1-54: Intonation and Pronunciation of "That"
That is a special case because it serves three different grammatical functions.
The relative pronoun and the conjunction are reducible.
The demonstrative pronoun cannot be reduced to a schwa sound.
It must stay .
Relative Pronoun
The car that she ordered is red.
Conjunction
He said that he liked it.
Demonstrative
Why did you do that?
Combination
I know that he'll read that book that I told you about.