Learn Portuguese (Portugal): É horrível que te estejas a demorar, enquanto o táxi espera! - It's horrible that you're taking so long, while the taxi waits!

Just like in English, the continuous form emphasizes an ongoing action happening right at this exact moment. Using estejas a demorar stresses the immediate, ongoing frustration of you taking so long right now, whereas demores would sound more general, like stating that you generally tend to take a long time.

Why is the reflexive pronoun te placed before the auxiliary verb estejas?

The word que acts as a magnet that forces the pronoun to go before the conjugated verb. Because of the que, the te must jump in front of estejas, rather than attaching to the end of the infinitive as demorar-te.

Why is demorar used reflexively here (te estejas a demorar) instead of just estejas a demorar?

While both demorar and the reflexive demorar-se mean to take a long time, using the reflexive version when talking about people emphasizes the person lingering, dragging their feet, or actively delaying themselves.

Since the first half uses the subjunctive, why is the taxi's verb (espera) in the normal present indicative?

The subjunctive in the first half is specifically triggered by the emotional value judgment É horrível que. The second clause is introduced by enquanto and simply states an objective, concurrent fact: the taxi is actually out there waiting. Therefore, it stays in the indicative.