Device connectivity depend on the device almost completely.
In your case, it seems that when you turn off the screen on the smartphone, the device is disabling all radios in order not to drain the battery instead of entering a reduced power mode listenning only for the packets been directed to his MAC. When you turn your screen on, it enabled the Wi-Fi radios back again and scan for previously know and preferred WLAN and joins again.
Have you tried to ping the device's IP address while in the idle state?
Unfortunatelly, this is something that is the manufacturer's hands and there is no way to do anything unless any new update on the device's OS fix it.
HTH
-Jesus
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