There are many strategies and tools for getting to inbox zero, yet they generally require a level of diligence most of us can't manage forever. Rather than doom yourself to failure, give into your inadequacies and stop aiming for zero.
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It's been found that diets often do not work because we've only got so much willpower and putting ourselves through heavy restrictions can only last for so long. That's precisely the problem with inbox zero strategies: they require a lot of willpower and you need to be very diligent to stay on top of your inbox. While some people are amazing enough to pull it off every day, a lot of us with highly trafficked mailboxes and to-do lists just can't do it. Something comes up and the inbox takes a backseat for a couple of days. Suddenly, the inbox is unmanageably full again and it's necessary to do another thorough cleaning. Stressing about a pristine and empty inbox doesn't help anyone, so instead of chasing that magic number you might want to consider ignoring it all together. Instead of Inbox Zero, try Inbox Infinity.
This is a very simple concept: don't bother emptying your inbox. Don't worry about reading every message. Don't organise anything you don't feel like organising. This is not to say you should simply give up on managing your inbox altogether, but that organisation may not be necessary. If inbox management stresses you out, stop managing your inbox.
The question then becomes "how do you stay on top of your emails and to-do items?" The first answer is already pretty well highlighted in Google's Priority Inbox because it's a feature that tells you what is important and what to ignore. You don't need to actually use Priority Inbox, but take a note from its playbook. If your daily inbox content is greater than the time you have to complete it, you need to start ignoring things. Many emails are easy to ignore because they're either ads, newsletters or other mostly unactionable items.
That doesn't necessarily solve the problem, however. While you don't want to explicitly ignore emails, you do want to choose what's most important. Star your emails, or mark them in a way that designates them as important, and then block out a few chunks of time during your workday to answer them. If you have any extra time, you can get to the less important emails. If you don't, ignore them. It's not necessarily the nicest approach, but your sanity is a bit more important than getting back to every single person that contacts you. As an added benefit, you set expectations: you cannot answer every email you get. As people come to notice this they will either email you less or find better ways to get ahold of you.
While this idea won't necessarily work for everyone, neither does inbox zero. You have to find a method of getting through your daily emails and tasks that works well for you. I feel that having realistic goals is better than idealistic ones I'm never likely to achieve, so I try to find ways to work with my flaws rather than pretend they don't exist. In some cases I find it very easy to organise things, like my Dropbox, but email is an exception. The important thing is that you figure out what's right for you.