Any 411 on this issue yet, folks?
Discovered definitely today I'm having identical issue to OP.
Initially, I wasn't sure. Since downloading Safari 6.1 (running Mac OS X 10.7.5 on a late 2007 Macbook), I hadn't used any of the customary in-browser/web-based photo editors I use until yesterday. Even then, I wasn't certain the "new and improved" Safari was the problem because I was experimenting with sites I don't normally use -- EWC Presenter, Kizoa, Animoto, et al. Hence, I assumed the non-functionality issues were with them and not at this end.
However, today, I used a trusty old friend, Pixlr. The process seemed to run smoothly while I was editing the photos. Yet, despite the site indicating via their usual pop-up window that the edited photos were being downloaded to the desktop, I got nothing. Nada, zip, zero. Tried again with a different image. Same problem: all functions seem a go, until I opt to d/l the edited photo to desktop. No image d/l'd. A complete, thorough search of all files, visible and invisible results in vapor.
Summarizing the issue:
~~ Safari 6.1 (and I'll assume Safari 7, too) will allow a user to log into web-based/in-browser image editors, but then at some point that apparently varies from site to site, the functions within the editor page cease to respond.
In other words, the new and improved Safari is **not** playing nicely with image editors.
The table is open for discussion! 😕