From searching online, there seems to be many potential causes for this, including on the Mint Forums.
Try running the following command:
sudo shutdown -P now
If this shuts down your machine properly, then it may be an issue with compatibility with your physical power button (if that is what you are using to shut down your computer when you have the issue).
In that case, try:
sudo apt-get update && sudo apt-get install laptop-mode-tools
This will install laptop-mode-tools which may install enough laptop config settings to allow Mint to poweroff elegantly. After install, choose laptop mode.
If that does not work, then set ACPI to not route IRQs. A captured IRQ that the kernel doesn't release could cause BIOS to always cycle rather than power off. Using you choice of text editor as superuser (in this case I used vim), add "acpi=noirq" to GRUB as follows:
sudo vim /etc/default/grub
Find the line starting GRUB_CMDLINE_LINUX_DEFAULT and add acpi=noirq to the end between the quote marks so that it resembles:
GRUB_CMDLINE_LINUX_DEFAULT="quiet splash acpi=noirq"
This change cannot take effect until after at least one full reboot cycle, so don't expect it to power off your machine the first time. If problem remains, then reverse procedure and take out the change. No point in diminishing functionality if it doesn't do anything.
Lastly, if any of the above possible fixes do not work, take a look at your BIOS power management settings, including (but not limited to) ACPI and APIC as this may be the cause. Alternatively, you can try updating you BIOS which may also provide a fix.