If you set your MC Server not to sleep Gizmo should be able to reconnect to it.
Gizmo will wake a sleeping MC Server when both are on the LAN using the Wake On LAN (WoL) process, but when you are away from home your phone is on the internet, and the equivalent Wake On WAN (WoW) process usually doesn't work. Some ISP supplied modem/routers always block WoW network packets and you will never be able to get it working. Some modem/routers just need configuration to allow WoW Magic Packets through the Firewall, and to be broadcast on the LAN, which then wakes the MC Server.
There are many threads discussion WoL/WoW, Port Forwarding, Magic Packets, and waking a server, if you want to try to get it working. Or just leave your server running all the time,