Outbox, or Sent Items?
There is a limit on how many messages can be in any given folder. If you've kept everything from the beginning, Sent Items could well be full. You can create subfolders in Inbox, which I think gets around that limitation, but I've never tried it with Sent Items.
Outbox holds only messages that have been sent but not yet read. Once read, they move to Sent Items. I'd be very surprised if Outbox were full, unless you're in the habit of PMing the deceased/permabanned/inactive
But I've been wrong before...
My friend and I applied for airline jobs in Australia, but they didn't Qantas.