Hi,
there should no big difference between offline and online usage, but it might be the case that the offline app itself is using also some memory by itself, so that there is fewer left for the browser webview.
Regarding iOS 7 please note that iOS7 itself is pretty unstable. Some crashes in iOS7 are unfortunately normal, many normal web pages or PDF files are also often crashing. Here Apple itself would need to provide a fixed stable version. E.g. - compared to iOS7 getting a crash in iOS 6 should be almost impossible.
The default memory limit for the tile images in krpano for iOS is already pretty low - just 40MB - see here:
http://krpano.com/docu/xml/#memory
And if you want you can reduce the memory need even more (e.g. by <memory maxmem="26" devices="iOS7" />) and eventually also reduce the
multiresthreshold setting to reduce the requested resolution.
Also keep an eye on your custom images in/on the pano or the website - e.g. to calculate the memory need of your images in MB do: width x height x 4 / 1024 / 1024. Try to use as few memory as possible.
Best regards,
Klaus