If you statically configure using the same settings from the DHCP scope, can you achieve internet connectivity? Usually it's a default gateway or dns problem. If you're using a different subnet for the static IPs than for DHCP, then you need to make sure there is a router interface for that subnet on that vlan (router interface = default gateway).
If DHCP is ok then you can increase lease times to keep an IP address longer (usually 8 days is the default but yours sounds much shorter) or you can create reservations which map an IP to a Mac address so that any time that Mac sends a bootp request for an address the DHCP server will give it that IP and will ensure that the IP is not given to another client.
