Hello Rakesh,
I've given a look at your show tech but I didn't find useful information for understanding why the eBGP session is going down when one link of the PPP bundle fails.
Edit:
If I understood correctly you say that everything is fine but if one member link fails in the ppp bundle the eBGP session fails and doesn't recover automatically.
I would suggest you the following:
verify ip connectivity between the two BGP endpoints that are the multilink PPP ip addresses.
use an extended ping of 50000 packets of size 100.
If successful repeat with packets of IP size 1500.
You can verify the state of ppp multilink with
sh ppp multilink.
During these tests try to tear down a member link to emulate a fault
What happens to icmp packets ?
After some timeouts you get again successful responses or they are stucked to timeout ?
You can also use a BGP debug to see why the session is closed and by which side
debug ip bgp events
do it in a different time
see
http://www.cisco.com/en/US/docs/ios/debug/command/reference/db_h1.html#wp1068563
Another suggestion, but if the router is in production requires some thoughts before, is to try to disable CEF on the multilink and on the member links, this just to see if there is any change in behaviour.
Hope to help
Giuseppe