What are the reasons that emails for a request for reference might be ignored or delayed in response, a long time after the deadline by an intimate academic advisor?
Professors and other researchers are typically busy people receiving a constant flood of emails in their inbox, a great many of which are time-sensitive and important. Yours is only one of many.
The most likely reason for somebody's failure to respond promptly to an email, then, are just the typical ones for any busy person: getting lost in their inbox, technical failures (overactive spam filter, address mixups, dodgy forwarding systems), and falling through the cracks in an overcrowded schedule.
It might also be, however, that the professor is wasn't actually as strong a reference as you thought and just didn't feel comfortable saying no. Did you ever have a non-email conversation about the references? And if they aren't responding to email, pick up the phone and call!
Finally, since this is not an uncommon occurrence, I also recommend that for important but asynchronous interactions like references, if possible one should give 1-2 more than required.