Not just quilt shops, but in any business. Well run businesses can and will do fine. I talked to a local guy who has an antique store and upholstery business. He pointed out that if you work (and I don't mean show up for a paycheck but actually work), hustle, show some ingenuity, there is a TON of work out there for the taking. He has noticed no slowdown.
Those stores with a good business model and that have built up a loyal clientele will do just fine. For example, I dropped off my sewing machine for service a week ago, and picked it up a few days later. She always gives a really good chocolate bar with a repair. She saw my husband was with me, and gave him one too. It's not a big thing. But it sure makes him not so fussy if I have to stop for some fabric!!!
From what I have seen, those stores that were on the edge prior to this temporary slowdown just can't pull it off. They were weak to begin with. Those that were doing well are doing ok and looking for ways to grow their businesses. When things fire back up, and they will, they we be poised to do very well.
Business failures are part of the business cycle. When a business fails, it's assets are purchased at a bargain by someone else with an idea. Getting a good deal on store fixtures and inventory may be all that's needed to get a good business model a fighting chance and an opportunity to succeed!