The 4th gen shuffle has a button-lock feature. See page 21 of the user guide (Lock and unlock the iPod shuffle buttons)
https://manuals.info.apple.com/MANUALS/1000/MA1550/en_US/iPod_shuffle_2015_user_ guide.pdf
If that's not the problem, try resetting (restarting) the shuffle. For a shuffle, a Reset is putting the power switch in the OFF position for at least 10 second, then turning it ON.
If that does not help either, you can try doing a Restore on the iPod using iTunes. This erases the iPod, reinstalls its software, and sets it to default settings.
Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings - Apple Support
If the problem is not fixed by the Restore, the iPod probably has a hardware problem.