Q: After sleep mode my computer sometimes doesn't recognize the wireless connection.  Is there anything I can do?

Solution may be found if you search in the "More Like This" section over in the right column.

There are quite a few.  Take your pick until you find one that works.

Change your router channel.  Sometimes this is all you will have to do.

Power cycling the router.  Read the router's user manual or contact their tech support for instructions.

System Preferences/Internet & Network/Network

Unlock the padlock

Locations:  Automatic

Highlight Airport

Click the Assist Me button

In the popup window click the Diagnostic button.

System Preferences/Network- Unlock padlock.  Highlight Airport.  Network Name-select your name.  Click on the Advanced button.  Airport/Preferred Networks-delete all that is not your network.

Place a check mark next to "Remember networks this computer has joined."  Click the OK button and lock the padlock.  Restart your computer.

http://support.apple.com/kb/TS1920 Mac OS: How to release and renew a DHCP lease

No internet connection (wireless)

Check to see if an extra entry is present in the DNS Tab for your wireless connection (System Preferences/Network/Airport/Advanced/DNS).

Delete all extra entries that you find.

Place a check mark next to "Remember networks this computer has joined."

Other resources to check into:

Troubleshooting Wi-Fi issues in OS X Lion and Mac OS X v10.6

Netspot

How to diagnose and resolve Wi-Fi slow-downs

Pv6 troubleshooting

Mac OS X 10.6 Help:  Solving problems with connecting to the Internet

What Affects Wireless Internet?

Solutions for connecting to the Internet, setting up a small network, and troubleshooting