Video app becomes corrupted after streaming iTunes purchases

Question

I wasn't sure what to use for a title here, but chose this because it captures much of what I am seeing.
Hardware:
3rd gen iPad, 32GB, iOS 7.0.4
What I am doing:
I purchase TV shows and movies from the iTunes store, but as we watch them while on the home Wifi network, there is no need to download the content to a device before viewing. Once a TV show or movie is purchased, it can be viewed in the Videos app as streaming content, much the same way that it does on Apple TV (which doesn't permanently store anything).
Key observation: I usually make these purchases through the Videos app itself, rather than going explicitly to the iTunes Store app. I am not sure this makes a difference, but it may.
What happens:
It all works well for several weeks or months. Then 3 bad things happen:
1) During this time I observe that the available space on the iPad steadily decreases (viewed through Settings -> General -> Usage). It starts with a value of approximately 12GB free space, and then declines, despite the fact that I am not storing any media files locally. After approximately 2 months, I now have 5GB free, and cannot account for the "missing" 7GB, not even close.
While it is to be expected that any streaming device must temporarily store content, that content is usually cleared after viewing or after some predetermined time interval, etc. I do not expect this content to simply accumulate endlessly.
2) Eventually, videos will fail to work properly. I will attempt to watch a purchased item, and it will run painfully slow, and may be missing audio. I check Usage, and my free space continues to decline. Subsequent attempts to view TV show and movies are now unreliable.
Big clue: shows that do not work properly cannot be deleted or downloaded locally.
3) The entire iPad becomes notably slower and less responsive running all of my usual apps (Pages, Numbers, Facebook, etc.)
What I tried that was illuminating:
I noted that under Settings -> General -> Usage, it shows the Video app as containing "No data". So, I tried downloading a different purchased video in order to guarantee that there is some data. While this video plays within the Video app, I observe that Usage still shows the Video app as having "No data", which is verifiably untrue.
Conclusion: the database used by the Videos app is failing to purge old streamed content, becoming corrupted, and now failing to report data storage to iOS.
What works:
Sadly, the only cure for this problem is a complete erase/restore of the iPad from iCloud backup. When I do this, all of my "missing" storage returns, and videos work normally. The iPad performance returns to its usual snappy self. But the cycle repeats, and I must eventually go through the 3+ hour restore process again.
This solution is 100% consistent with a corrupt database, and hence I suspect that the Video app is the culprit, consuming space until other systems are affected.
Has anyone else seen this?

Answer 1

I'm experiencing this exact issue on two devices:
iPhone 4S 32GB
iPad Air 64 GB
Both while running iOS 7.03 and 7.04 (recently updated both devices to 7.04 hoping it would help. It didn't)
My iPhone had become nearly unusable until I found your post. It had apparently accumulated >12 GB of "temporary streamed content", as after I did a backup/wipe/restore, I had recovered to around 12 GB free space.
It's unfortunate that the fix requires a complete reset/restore cycle, as it's very time-consuming, but thanks for providing that fix! It saved my iPhone 4S. Now I can comfortable wait until the 6 comes out to get a new iPhone.
Really, though, this seems like a critical bug for iOS devices. I'll certainly not stream any iTunes content until/unless this is fixed. I found that if I turn off "Show all Videos" in the Video App settings, it doesn't show the iTunes cloud content for streaming from within the App. This forces me into iTunes to do a full download if I want to watch something. Kind of a pain, but it beats a device that's maxed out on storage and basically bricked.