One of the more commonly reported complaints about the iPhone's SMS scheme is that there's an artificial limit on the number of text messages that can be stored. In other words, though there may be a significant chunk of free memory on the device, the amount of text messages that can be stored is capped. This can result in the message "Your SMS mailbox is almost full. Please delete some messages."
Apple has now revealed, in Knowledge Base article #306427, that the limit for SMS messages is 1000, adding:
"If iPhone indicates your SMS mailbox is almost full, just delete some SMS messages. You can delete a conversation by swiping left or right over a conversation and tapping Delete."