Mobile Ad-hoc Network is a network with autonomous nodes. The MANET is a selforganized, auto-configure network and the mobile nodes have been free to move. To enable the MANET to connect to the internet it uses an intermediate bridge called a gateway. The MANET and the internet gateway is a heterogeneous network, which needs a gateway discovery mechanism. There are three types of gateway discovery mechanism known as proactive, reactive and hybrid gateway discovery mechanism. The main challenge in the integration of the MANET and the Internet is, there are high link disconnection results from node mobility and limited energy. Furthermore, there are a high handoff, link disconnection, packet drop, end to end delay, and small packet succeed delivery. The purpose of this study is to examine the impact of node mobility and energy in the stability of path in integration of the MANET and the internet. In this study, the AODV routing protocol is used and modified to examine the gateway interconnection of the MANET and the internet. Moreover, the AODV control messages RREQ and RREP and the routing table is modified to store the energy factor, signal factor, path queue length and stability factor of the path. The proposed gateway discovery algorithm is known as stable AODV(S-AODV), The stability factors the path from the source node to the gateway, calculated using simple additive weighting method of the signal factor, energy factor, average path queue node and the path with the minimum signal factor is the more stable path. The proposed S-AODV algorithm has shown up to a maximum of 21% enhancement in PDR and it has minimum node handoff, disconnection time, End-to-End delay and routing overhead over hop count based AODV gateway discovery and the result shows that in the large simulation area using stable based gateway discovery is a better achievement.