You ask "So, Will the connection be reset if the any of the endpoint IPs change? If yes, we can not keep existing connections intact if one gw goes down, but at the same time new connections will be routed through next available gw. "
The only way to have this work correctly, 100% of the time, is to use BGP. You may wish to ask your ISPs (one or more of them) if they will set up BGP for you.
With BGP you would "announce" your IP address block and the various ways to reach your servers via the 3 different ISP connections. You would have 1 set of IP addresses that all 3 network connections would "know" how to reach.
Traffic would automatically switch to using whichever is closest from a network standpoint while all 3 connections were up. If one or two connections went down, traffic would still reach your server via the connection that was still working.
If you are paying more than 1000 USD or Euros per month in connection charges, then you are paying enough to merit setting up BGP, and your ISP should be able to help you for free or at a low cost. If instead you are having different connections but are using low-cost, low-speed links like DSL, then the ISP will probably not assist you.
