Check the advanced options in Wi-Fi menu of settings, maybe the Wi-Fi sleep policy settings are set to OFF whenever SLEEP/SCREEN OFF. Change it to ALWAYS ON, or NEVER WHEN CHARGING. Tends to drain the battery a lot more, if set to always on. I use wifi manager by Kostya Vasiliyev (available in the Google play store) to get fast WiFi lock-on after screen on/wake.
Sent from my Transformer TF101 using XDA
Xperia Z C 6603; Stock LB, Root (101 F/W) (Son's)
Xperia Z C 6602; Stock LB, Root (101 F/W) (Wife's)
Moto E XT1022; Stock (Mine)
Nexus 7 (2012); EHNDROIX-V, Root (Son's)
Dell Venue 7 (2013); Stock 4.3, Root (Ours)
Asus TF 101; ARHD, Root (Mom's)
KitKat FAIL! Stick with Jellybean!