There are a ton of reasons I can give you:

You aren't getting her engaged in the interaction enough.

Your communication skills suck.

You aren't taking the lead in your interactions...

BUT

The most common reason I see interactions going stale is because there is no established reason for the damn interaction.

If the girl doesn't understand WHY she's involved in this interaction, why is she continuing to be a part of it?

A great example that I heard recently was:

If you're about to buy a car, and the car salesmen comes up to you and starts asking you about your day, the weather, your family, your shoes, etc.

But NEVER TALKS ABOUT CARS

You're probably going to be pretty annoyed some point early on in the interaction.

Why?

Because he's WASTING YOUR TIME!!!

There's no actual reason for you to be having this conversation unless he's planning on selling you a damn car.

So, set the tone of the interaction early on.

Establish the man-woman frame (why you're there in the first place) and, maintain that premise THROUGHOUT your interactions so the girl understands why she's there as well.

What set's the tone of the interaction?

Your tone of voice

Your physicality or lack thereof

Your eye contact

Your non-verbal communication

The content of the conversation itself

Establish the tone of the interaction and you'll find that significantly less interactions are "going stale" because should always at least be a REASON for the interaction.

Hope this was helpful!