I've given up on inbox zero -- I now use inbox infinity. Everything stays my inbox unless auto-categorized (mailing lists, specific clients, etc). When I look through my emails, I flag any email I'm not dealing with right now. Otherwise I reply, leave it, or delete it. I archive anything old than 6 months every 6 months.
I suppose, in effect, my list of flagged emails is my inbox-zero but I feel more connected to whole stream of email with the box full. I occasionally need scroll to previous days and glance around.
I also have a Pebble so I'm effectively checking email instantly all the time. I find with the pebble that I dismiss things much more frequently now (emails, texts, and calls). Perhaps because the act of looking at the Pebble is so passive compared to checking my phone or computer.