Galaxy Tab 10.1 doesn't keep wifi connected despite settings
In a nutshell: using a static IP is like owning a house.  Having a DHCP lease is like renting, but you may have to move when the lease is up.  Unfortunately, the Tab's implementation is like a renter who leaves, then tries to get back into his old apartment (which in this analogy is a dynamically assigned IP address on your WiFi network) and finds it locked.  Instead of asking for a new lease, it just keeps knocking on the door, never to enter.  In this case, it means that your Tab won't connect to your WiFi network on wake.

The detailed explanation: It looks like Samsung's implementation of DHCP lease renewal is at fault here.  When a device wakes up and then tries to connect to WiFi, it will ask for a DHCP lease (if expired), which also gives it a dynamically assigned IP address.  This works fine when the Tab first connects.  However it looks like it never asks for a new lease and thus new IP address.  Instead it caches the IP address and keeps trying to reuse it.  DHCP is dynamic so it means that any particular device on the network cannot rely on a specific IP.  So eventually the lease will expire and/or the IP address that the Tab is using gets reassigned to another device.  When this happens, your Tab cannot connect to WiFi.

So the solution is to assign static IP until the Tab's implementation of DHCP lease renewal is fixed.

An alternative solution is to root your device.  Then you can manually delete the cached file which contains the stale IP address following the instructions at: http://steve-shaffer.com/2011/02/samsung-galaxy-tab-wifi/ (where I learned about some of these details as well).  This will cause the Tab to renew the DHCP lease properly and live in a brand new and shiny dynamically assigned apartment on your WiFi network.