This question is asked often in Ask Ubuntu, sometimes with few hints about the situation.
There are many reasons a persistent USB might not boot
BIOS
USB not set as first hard drive in BIOS
Problems with BIOS or UEFI boot partitions or files.
Secure Boot not turned off
Drive not compatible with computers BIOS or UEFI boot mode
Incorrect partition table
Out of date BIOS/UEFI firmware
Junk in volatile memory
GRUB
Incorrect root partition in grub
Incorrect path to ISO in grub
Incorrect persistent-path, (if used), in grub
Grub menuentry structure not suiting OS
Incorrect file type for vmlinuz and initrd (.efi and .lz)
The word "persistent missing from grub.cfg, txt.cfg, syslinux.cfg or text.cfg
PERSISTENCE (CASPER-RW & HOME-RW)
Persistence partition is not ext file system
Persistence file not on FAT filesystem
Persistence file/partition reused from different version
Persistence file full of data, or file update attempted
HARDWARE
Corrupted flash drive
Bad flash drive
Not enough RAM to run Ubuntu
Bad or incorrect USB socket
Incompatible computer CPU
Incompatible computer GPU
Computer does not meet minimum specs, lighter version of 'Buntu required
Motherboard voltage irregularities
Motherboard BIOS limitation with multiple USB devices
Computer does not boot USB's. Plop boot manager required.
SOFTWARE
Bad MD5SUM / Corrupt ISO file
Modified or corrupted ISO9660 partition
USB removed from computer before ISO file is completely copied
Out of date Boot drive creation tool
User inexperienced with boot procedure
Please let me know of any reasons I have missed.
An up-vote for any currently valid original reason not on the list, A green check for best original list additions