This is my note about ASA IPsec Site-to-site behaviour that I found. The VPN tunnel is down when there is no traffic between the two site (A to B), even when you have configure it.
The solution is simple, just send a simple traffic such as ICMP ping to any private address in the other end, for instance 10.10.10.30.
When the tunnel is required, it will be activated automatically.
To make sure you can issue this command to view the tunnel:
show isakmp sa