Hi,
1: How frequent VPN flaps ? Does the peer device support the VPN monitoring, what device is that ? https://kb.juniper.net/InfoCenter/index?page=content&id=KB3988
2: Each ESP packet will have sequence number, if you can capture the ESP packets on both side and see the missing sequence number then it's getting lost in the Internet, or may be by ISP .
3: You can also keep the tunnel stable (by disabling the VPN monitor) and have some test traffic( e.g. ping) running between two machines over the VPN, and check if there are frequent drops despite VPN is UP. Still , step 2 is the best way to check the ESP drops.
Thanks,
Vikas