BusyBox on persistent USB Livesystem
I don't know exactly what causes the boot to terminate in a busybox/initramfs prompt but I can provide you with an alternate solution that does not involve installing Ubuntu to USB and still gives true persistence.
Try to use the mkusb tool to make your persistent USB system.
Detailed instructions are given here.
Complete documentation+working can be found at https://help.ubuntu.com/community/mkusb