When the backlight that illuminates the flash's display panel goes dim, the settings should still be showing on the LCD panel as long as the flash is active. If they're not, then something is wrong with the flash. You can try shining a flashlight on the LCD panel after the backlight goes out and see if information is still being displayed (just without any self-illumination).
Although there is a setting available that tells the LCD backlight to turn off after about 15 seconds, there is no menu option that tells the flash to go into sleep mode after only 15 seconds. The shortest time selectable via the menu for the flash to go into sleep mode is after three minutes of idle time. If your flash is going into sleep mode or shutting off in less than three minutes with fully charged batteries installed then there is something wrong with your flash and it is not behaving as it is supposed to behave.
Yongnuo flashes have a less than rock solid reputation regarding reliability and longevity issues. I've had a couple that flaked out on me in different ways. They usually start by doing something odd here or there. A simple power cycle will usually solve the problem for a while until it reappears on an unpredictable intermittent basis. Then they'll start doing it more often and other unexpected behavior might manifest itself. This will get progressively worse until eventually they become unusable.
It's often the price one pays for going with cheap, third party flashes. If having a functional flash is critical for a shoot, I advise people to have at least one brand name flash made by the same manufacturer who made their camera. If additional flashes are needed, then third party units can be a good way to go as the cost savings are significant. Just always be prepared for one of them to die on you at the most inopportune time and always have one more flash than you need with you. It won't happen very often, but eventually it will happen.