In any case, it seems unusual if they are actually using a mail client. They should be using a CRM software that fetches mails from their support ID and feeds it into a database for record keeping and status management. In any case, Airtel now just calls you back instead of asking you to mail them with your complaint to process things faster.
They fixed the My Airtel login issue within a few hours. Reliance took weeks to fix a similar issue.