I have same problem. In my board and arduino-Due-schematic.pdf Vddout for core supply use 2x10 mkf capacitor - more than enough (in datasheet ATSAM3X8E for Vddout is offer 4,7 mkf capacitor).
For this reason may be violation of time in initialization flash and boot from SAM-BA .
I've attached a condenser 3000 mkf and board has been successfully starting with power outages in 5 minutes instead of 10 seconds. Now I'm thinking to delete one capacitor 10 mkf, I think this will solve the problem.