The reset doesn't work. I completely factory-reset my device, then restored it from backup. But before I restored it, I ran through a few scenarios involving Safari, Google Maps, and a few other apps. It was marginally better initially, but I soon got it down to things regularly refreshing every third app swap or so. I restored my backup and I was right back to where I was before the wipe.
I've found that things get worse the longer it's been between hard resets. I haven't taken the opportunity to hard reset for a few days and I can rarely switch between two apps without the second app fully refreshing. Yesterday I pulled up a location in Google Maps and started my route. I switched over to the Podcasts app to start my podcast. I then switched back to Google Maps and the map refreshed. Now THAT makes for a useless "smart" phone.
This is not some glitch that can just be cleared with a reset. It's a case of a new OS needing more memory and not managing memory as well as the previous version. As I ran through my own memory state logging, it's clear that the 512 MB of RAM on these older devices is nowhere near sufficient for iOS 7. That's why we're not hearing as much from those with the newest 5's and iPad Airs, which have more memory. But it is still seen with those, just at a higher threshold, so there's still an underlying problem - the extra memory just masks the problem.
I've done some reading through various links provided here and via my own searching. The Apple article on memory management listed by tonyjambo had a sentence that caught my eye: "Writable data is never removed from memory by the operating system". If this type of data is not being managed correctly, it may grow to a point where there's no space left for other apps.
iOS 7 has obviously changed the formula for how this memory management works, and these refresh problems are the result of a combination of general poor memory leak management, poor management of this writable data (resulting in the need to shut down other apps), and overall increased memory footprint from all the graphical "fluff" and other bloat in iOS7.
As a product manager for a very large tech company, I agree with the assessment that this issue should never have made it out of the QA cycles. Bugs, even known bugs, are always going to ship with a release. But some bugs are more difficult to fix than others. My guess is that it was probably identified - there was too much testing and there are too many smart resources at Apple for me to believe they didn't find this - but the decision was made to let it out the door anyway. I think the difficulty of fixing the issue, the delays it would have incurred, the desire to get as many devices on iOS 7 as possible, and perhaps a conclusion that the issue wouldn't affect users to the degree this is, led to the decision to ignore it. I'm not big into conspiracy theories, but I wouldn't rule out that some may have seen it as a way to "nudge" owners of older devices to new ones. Regardless, it was the absolutely wrong decision to ship this with the recommendation for older devices with less than 1GB of RAM to upgrade, and I'm sure they'll lose a significant number of users over this.
Unless the Apple engineers can conjur up some magic in how memory is managed in iOS 7, we're all SOL. But that's the only way I see this getting resolved, as iOS7 isn't going to shrink anytime soon, and Apple isn't going to offer to up free RAM upgrades for those of us stuck with 512 MB.
Good luck to those of you contacting support. We all appreciate your efforts. I'm just not holding my breath. I was contacted proactively by Apple from my posts on the other thread and sent them logs, etc. But it's been almost a month and I haven't heard a peep from them since. I think I'll be stuck with this pain until I hit my 2 year contract mark in a few months. At that point, if this situation isn't at least acknowledged by Apple, I'll cut my losses in platform investment and look at another option.