It is possible that your router(modem) given to you by bsnl could be the culprit. I suffered the
same problem till recently. After changing the modem it got sorted out. BSNL staff are ignorant and will shy away from modem and splitter troubleshooting.Observe the Modem at the time of failure. The sequence may be first power light goes and USB light turns on for a moment, soon power light returns and the DSL light unset.