Does it shut down as in power off or does it reboot? The latter is a driver issue most likely and/or something corrupt in your OS. Is this Windows, and which version? Got all the latest updates and patches?
If it actually powers off and doesn’t reboot then it could be a hardware power issue. Is it a desktop, laptop/netbook or tablet? If it’s anything working off battery, has it got enough charge, do you leave the Garmin plugged in a while as it will charge off the computer which will drain your battery and shut down?
As for the 510 and Bluetooth, good luck with that. Bluetooth doesn’t work for a lot of people and takes forever to get it to pair properly.