There can come a point in any inbox/process/outbox system, such as email, when the volume coming in simply outpaces your processing capacity. I call it the "firehose point". When you simply get too much email to handle, what can you do? It's not a matter of "time management" at that point, nor of getting more efficient at handling individual emails, because any time management or email handling strategy you employ can be overwhelmed again by more volume. I mean the point when, no matter how quickly you handle any item - even to delete it - by the time you're done, at least two more have arrived.
The only possible response at that point is to accept that you will never see everything. Some people handle holiday email with a kind of declaration of bankruptcy: select all, delete, rely on second-notices if it's important. People do the same on social media, only reading the most recent items. It's an acceptable strategy, in its way, but you really should only apply it to situations where it doesn't matter if you're uninformed.
Mokalus of Borg
PS - Of course, if you happen to miss the second notices, too, you've got bigger problems.
PPS - Assuming you have real responsibilities managed this way, that is.