I've used a 1GB flash drive and because of the sheer volume of the ISO image compared to the space on the drive creating some persistent space is not only next to impossible it's also just not feasible because you'd have a VERY small amount of space for stuff to save off to. Grab a 4 to 8 GB flash drive, put on the ISO using the Ubuntu built in USB startup disk maker and it should work. At least it did for me.
One other thing you can also try (I've done it so it should work.) is take an external HD that you can plug into the system via USB (Like a Western Digital backup drive for example.) and then what you do is take out the HD from your pc, plug in the external one into the usb ports, and then you (should be able to) install to that external drive from the ubuntu install menu. Then when you're all said and done you've got an external hard drive that is persistent because well, it's a whole OS!
I would also recommend that you take a look at the following link/question. It goes into a bit more detail on how to do what you're asking... Points down to the link
Install Ubuntu on USB Flash Drive or USB powered external HDD?
The above answer is probably the simplest but if you want more than 4GB persistence:
Boot Live CD or Live USB.
Plug in flash drive.
Start gparted.
Create 2 GB FAT32 partition, (on the left side of the bar). (size is optional, extra space can be used for file storage and transfer to Windows machines).
Create a 4 GB ext2 partition to the right of this, labeled it "casper-rw". (ext3 and ext4 also work).
Create a partition in the remaining space and label it "home-rw". (optional, creates a separate home partition)
Close gparted.
Un-mount and re-mount flash drive.
Start "Create a live usb startup disk", (usb-creator).
Select "Discard on shutdown".
Press "Make Startup Disk.
When usb-creator finishes replace the contents of the file syslinux.cfg with:
default persistent
label persistent
say Booting a persistent Ubuntu session...
kernel /casper/vmlinuz
append file=/cdrom/preseed/ubuntu.seed boot=casper persistent initrd=/casper/initrd.lz quiet splash noprompt --
Shutdown, remove CD, reboot.
First time booting you can go to users and groups and create an account with yourself as an Administrator, with password if desired.
Note:
The above code will bypass the Try/Install and Language screens.
Best Answer
Are you on a UEFI machine booting 64 bit versions of 12.04.2, 12.10, or 13.04? If so you may be experiencing bug 1159016. Feel free to add yourself to the 'Does this affect me' list in that case. Presuming you really created the USB with persistence, you may manually turn it on by editing the
/boot/grub/grub.cfg
file on the stick, adding the wordpersistent
to the kernel line you ate booting.