An iframe just loads the page src specified. Once that page is loaded, it's really up to that embedded page to handle it's loading. Meaning: once we specify iframe and src to in our app tab, the processing of that embedded iframe page is handed over to that embedded page.
I am guessing MailStore Web Access is using an iframe as well, which should be fine since nested iframes are valid in HTML.
So one thing that came to mind: I just posted an update to the zimlet to make sure we are closing our iframe tag and giving it a name. That might be confusing the nested iframes. So please check out the latest zimlet code here:
ZCS 6.0:Zimlet Developers Guide:Examples:Tab iFrame - Zimbra :: Wiki
If this doesn't do the trick, you might want to check with the MailStore guys about running their Web Access client in an iframe.