I have run Atomic Web for many years on my iPhones (3, 4, now 5). However, when I upgraded to iOS7, when I hold a link, the menu no longer comes up. Nothing happens. I haven't been able to find any setting which would change this. Is there something new with iOS7 which I didn't know about before upgrading?
I downloaded the app to test what you were taking about, and I can confirm the issue. They last updated the app on November 20, 2012, so this is most likely a bug that will need to be fixed by them. You can try to contact them at firstname.lastname@example.org about the issue.
I have the same issue in iOS 7 on both iPod 5 and iPhone 5s. I contacted the developer once or twice; I even tried posting a comment in their blog.
Ultimately I installed Mercury instead. I was able to export my Atomic bookmarks to Mercury and I moved most of my saved files and web pages into other applications. I keep Atomic around just in case it gets updated, because I still like how it does some details.