Bonjour setup question
You can not do this when the display is asleep. Unless an app is actively utilizing it, the WiFi radio is put into it's sleep routines relatively quickly. (I don't know how the 3G radio in the iPad works, so I can't answer that half of the coin.)
Outside of that, what is the actual problem at hand? Are you using some app that provides a webserver/other connection mechanism that you cannot connect to? Surely you're not concerned that you can't ping your iPad, only because you cannot ping your iPad.

Besides all that, I do want to confirm that it's possible.

$ ping ItsNew.local
PING itsnew.local (10.0.3.127): 56 data bytes
64 bytes from 10.0.3.127: icmp_seq=0 ttl=64 time=9.638 ms
64 bytes from 10.0.3.127: icmp_seq=1 ttl=64 time=398.883 ms
64 bytes from 10.0.3.127: icmp_seq=2 ttl=64 time=211.562 ms
$ ping Its-An-iPad.local
PING its-an-ipad.local (10.0.3.168): 56 data bytes
64 bytes from 10.0.3.168: icmp_seq=0 ttl=64 time=210.275 ms
64 bytes from 10.0.3.168: icmp_seq=1 ttl=64 time=130.986 ms
64 bytes from 10.0.3.168: icmp_seq=2 ttl=64 time=154.825 ms

No, neither my iPhone nor my iPad are jailbroken. Stock iOS 4.3.1.