In the Cursed Child, how did Snape get his soul sucked out if he had a Patronus protecting him?

Question

Here is the scene where it happens: Harry Potter and the Cursed Child Act 3 Scene 9:

SNAPE: Depulso!

UMBRIDGE is propelled backwards through the air.

She always was too grand for her own good. There’s no turning back now.

The sky turns even blacker still around them.

Expecto Patronum!

SNAPE sends forward a Patronus, and it’s a beautiful white shape of a doe.

SCORPIUS: A doe? Lily’s Patronus.

SNAPE: Strange, isn’t it? What comes from within.

SNAPE knows what this means.

You need to run. I will keep them at bay for as long as I can.

SCORPIUS: Thank you for being my light in the darkness.

SNAPE looks at him, every inch a hero, he softly smiles.

SNAPE: Tell Albus — tell Albus Severus — I’m proud he carries my name. Now go. Go. SCORPIUS, and then starts to run.

SCORPIUS thinks and then runs after the doe, and around him the world gets scarier. A bloodcurdling scream goes up at one side. He sees the lake and throws himself inside.

SNAPE readies himself.

SNAPE is pulled hard to the ground and then pushed high into the air as his soul is ripped from him. As the screams just seem to multiply.

The doe turns to him with beautiful eyes, and disappears.

There is a bang and a flash. And then silence. And then there’s more silence.

It’s so still, it’s so peaceful, it’s so perfectly tranquil.

SCORPIUS ascends to the surface. Breathing deeply. He looks around himself.

Breathing deep, panicked breaths. He looks up at the sky. The sky certainly seems — bluer than before.

In the bolded section, we see that the doe is still present even after Snape gets his soul sucked out by the dementors? Why or how then did Snape get his soul sucked out if the doe was still there?

Answer 1

It does seem, as @sumelic suggests, that the Patronus has a duel role in protecting Scorpius also, which is sure to limit its effectiveness - though it does return at the end.

But the key line is this:

"You need to run. I will keep them at bay for as long as I can."

Snape is surrounded by an oncoming force of Dementors and does his best to keep them at bay. We have seen our heroes fight off Dementors with just one Patronus but I don't think there is ever a suggestion that one Patronus from a lone fighter will mean all Dementors are chased away forever.

In JK Rowling's Pottermore writing on the Patronus she explains this as the work of the most exceptionally powerful Patronus ever:

Never forget, though, that one of the most famous Patronuses of all time was a lowly mouse, which belonged to a legendary young wizard called Illyius, who used it to hold off an attack from an army of Dementors single-handedly.

So while it can be done, Snape is a gifted wizard with a powerful Patronus but not the most powerful ever. And, of course, you'd have to admit that he has a rather shallow vault of powerful positive emotions to draw on in both versions of his life.