1) How often do you visit India? When are you planning to go to India next?
2) Are you still in India? If not, is the SIM in your possession or is it with someone in India? (someone who can put it in a mobile so that it is always connected to an Indian tower)
3) Have you provided this number to any services (like banks, payment services, Aadhaar, Passport, PAN, etc,.,) which might send you an OTP every now & then? Or do you need this number ONLY for whenever you go to India?
The cheapest possible recharge amounts that I may suggest might differ depending on your answers to these questions.
P.S:
No, I don't think Airtel might care about whether or not you're currently in India (meaning, your VISA expiry date). They should be happy as long you keep recharging the number.