Well there is your answer right there
Leave it on 24/7, each time you turn it on/off you will be getting a new IP, and so the idle time "0"/ keep alive is meaningless.
Try keeping it on a week, all the time, leave your idle time "0"/ keep alive as it is and see if your IP address changes, if it does then you know that BSNL give short leases on IP addresses.
Router only uses about 5/10W, so it won't cost a whole lot, but may get warm in summer, especially in India, so keep it cool if you can.
This explains better what I have been calling a short term static address, ie my dynamic IP with the router on 24/7...
"A sticky dynamic IP address is an informal term used by cable and DSL Internet access subscribers to describe a dynamically assigned IP address which seldom changes. The addresses are usually assigned with DHCP. Since the modems are usually powered on for extended periods of time, the address leases are usually set to long periods and simply renewed. If a modem is turned off and powered up again before the next expiration of the address lease, it will most likely receive the same IP address."