Garlic scapes keep FOREVER! I've left them for months - MONTHS - in the fridge, and they were still good! I've also left them in a bag in the kitchen counter for almost a month, and they were OK to use! We have air conditioning, though, so the house never gets really hot or humid.
Unfortunately, they take up a LOT of room, so I freeze them to use later, because I love them in pork chili, beef chili, bolognese, pasta, risotto, dressing, and mayonnaise.
Here are the instructions I followed: How to Freeze Garlic Scapes
Here's a photo of how our scapes look after almost a month at room temperature:
As you can see, the flower buds have dried out and some of the cut ends are also dry. I remove the flower buds and the cut ends. I drop the middle pieces into a bowl of warm water and run my fingers along each one to dislodge any dirt or debris. I transfer them to another bowl with cool water.
Here's how they look after they've been cleaned:
I remove 5-6 pieces at a time and slice them. Some I cut 3/4" thick, others 1/4" thick.
I seal them in 1-cup portions in vacuum bags, label them, and into the freezer they go for use until next spring.