I have a similar problem. My Nexus 10 /5.1 an Nexus 7/5.02 do not loose connection to the access point. But each URL-request takes a very long time. Starting a website takes about 15 sec on a 50 MBit DSL. Youtube viedeos stalls during streaming.
I found a workaround for my problem in a german forum. It seems that there is a problem with authentification on WPA2/PSK wifi connections in lollipop.
Here ist my workaround. Please check if this helps for you...
1) set yout wifi at the access point to WPA & WPA2 authentication. This will enable TKIP autentication on WPA.
2) Install an app "WiFi Advanced Configuration Editor". This will allow to disable AES authetication on WPA2 on your android device.
3) start app and select your wifi. Then open "Group Ciphers" und "Pairwise Ciphers".
4) with each of them deactivate all ciphers except the "TKIP"
5) Disable and enable again your wifi to load the new setup.
This TKIP setup limits your wifi speed to 54 MBit but without stalling ! Browsing and vidio streaming works flawless an speedy for me.
Pleas confirm that. Otherwise you have a different problem.