A quick prompt that does not appear is nearly always a display location or a saving problem rather than a fault. Check these in order.
The display location does not match where you are looking
The most common cause. A prompt set to Follow-up only appears after the visitor sends a message, so it is correctly invisible when you open a fresh conversation. A prompt set to Start only appears at the beginning, so it disappears once the conversation is under way.
Open the prompt and check its Display Locations. Select both if you want it available throughout.
You are looking for it near the launcher
Quick prompts appear inside a conversation. The messages near the chat bubble, before the widget is opened, are ice breakers, which are a separate feature with their own settings. If you expected something outside the widget, you are looking for an ice breaker.
The preview is showing saved settings
The Playground preview reflects what has been saved. If you added a prompt and did not save, or saved and did not reload, the preview shows the previous state. Save, then reload the preview.
You are on the live site rather than the preview
Your website may be serving a cached page. Open it in a private window, or force a refresh, before concluding the prompt is missing.
Still not showing?
Open the quick prompts list and confirm the prompt is actually there with the locations you expect. Then open a fresh conversation in the preview, check the start position, send one message, and check the follow-up position. Testing both positions separately tells you immediately whether this is a location problem or something else.