When the standby LB becomes active, one the URL doesn't respond though the boxes are in Sync.

Have you got MAC masquerade and / or vlan failsafe configured? Which version of BIG-IP are you on?

I am using BIG-IP 11.2.1 Build 862.0 Hotfix HF2 . Yes both the MAC masquerade and the vlan failsafe is configured coz all other URLs do failover, its only this one URL that doesn't , though the config for this URL is same in both the boxes.

Did you try to fail it back? There are a multitude of issues with versions of v11.2.*, and for v11.2.1, the hotfix releases are now up to 11 now: Hotfix-BIGIP-11.2.1-1292.0-HF11. You should apply it as soon as you can.

It works fine on Active. ok let me consider upgrading it, so you mean to say its a bug in this version ?

I cannot point a finger at anything right now, as there is a long list of bugs fixed since v11.2.1HF2 and I have not looked in it. You can check the release notes of HF11.