In the ipsec negotiation, proposals do the keys match for lifetime association and for any idle and session timeout. Also, the ipsec session may disconnect since it relies on interesting traffic. Without traffic going down the tunnel, it will close until some attempt to.
Grab the setting off both (when you can) and review them, ensure the lifetime of the connections are the same.
One test I would suggest, keep a continuous going from one side to another device on the other side, this should maintain the tunnel. And obviously, it plays a role which VPN you use. So make sure to read a VPN comparison from vpnwelt or any other trustful resource - depending on your preferences and needs.