If a simple ping/connectivity test is causing the circuit to have packet loss, then I would imagine virtually anything else normal traffic wise will cause even more trouble. ICMP is minimal traffic. Sounds like circuit issue to me
"I noted that when I receive lost packet due to the connectivity ping fail"
The lost packet was not 'due' to the connectivity ping fail, its the other way around. The ping failed because you have packet loss, back to the circuit having an issue in my opinion.