OK, I tried it out a bit more to try and narrow down the issue.
First off, it seems to be occurring only in the google chrome browser, and I have discovered that refreshing the page actually "fixes" the form and bypasses the problem, so it isn't such a big deal.
That being said I tried to narrow down the conditions of when the edit boxes stopped being responsive but I can't seem to get a series of entries/actions that consistently causes the behavior, unfortunately. It just seems that after a variable amount of quality/weapon entries and edits, the edit qualities box fails to respond and while it will allow you to select the add qualities box, these qualities will no longer apply to the stat block. As I said refreshing the page fixes it.
I will keep my eye on it to see if I can get any better info.