First, go to Site Properties --> Connection settings for your site profile and ensure that the setting for "Connect at login/startup" is enabled. Next, go to App Settings and ensure that "Run in taskbar tray at startup" is enabled.
If the issue remains, you can check the following items or use the work around listed below to connect to your site at login:
Check the registry setting HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\NetworkProvider\Order\ProviderOrder.
It should look like the following:
Make sure WDNP32 is first in the list.
Use command line parameters with WebDrive to map your drive, and create a batch file called "MapMyDrive.bat" using Notepad. Enter the following:
"c:\program files\webdrive\webdrive.exe" /s:"<your site name here>"
Replace <your site name> with your actual site name, then save the batch file and place the batch file in your Windows "Startup" folder so that it runs when you login.