iPad iOS 6.1.3 suddenly very weak wifi signal
I would ask if you can definitely link the introduction of the poor signal to the time immediately after installing the upgrade.  They may be linked, they may not.  If you think there is a link, then I would advise backing up the iPad, and reapplying the OS update via a full restore, thus essentially imaging the entire OS from scratch rather than relying on the OTA upgrade from 6.1.2.

After a re-image, then to rule out any configuration issues, try to connect to the WiFi source without restoring your data.  If it works, then perform a restore and check again.  If it's still not working, then my hunch is that maybe you have accidentally caused the wifi antenna connection to disconnect internally - serious question, can you identify any faint rattle type noise if you shake it, particularly in the bottom right where the cable connects.