If your laptop's lease for the static IP expires or is taken by another device while it's in standby, it would have trouble picking up the connection immediately upon waking up.

Do you have any other devices on the network that could possibly take your laptop's static IP? If there is, and you don't specifically require a static IP, you might be able to fix the problem by setting it to use DHCP.

Start > run > ncpa.cpl > Local area connection properties > General > Internet Protocol TCP/IP > Obtain IP address automatically