I also had this problem. I bought an iPad mini for my 8 year old son for his birthday. It connected out of the box but as soon as I updated to iOS 7.03 it would only randomly connect for a minute or two. I followed all suggestions from Apple Support to no avail. I returned it and got another. Same problem. Connects out of the box on iOS 6 but update to 7 and same problem. No Wi-fi. The solution was to remove all security from my wireless network and it connects just fine. Obviously a flaw in iOS 7 that Apple does not wish to talk about or recognize.
Thanks for taking the time to answer but what your're suggesting is a completely different issue. You're implying you have an intermittant wifi connection, i don't. I don't have an internet connection, that's my issue.
It only detects the internet connection once i'm sat on the router and its fine when it connects.
My issue is that it doesn't detect any wifi in range.