When you close any card, Axis will ask for the reason. Tell them that you are closing it due to very low limit. They will ask you to send IT returns or salary slip and blah blah blah. Don't give up. Tell them to give you LE based on history of usage of card or go ahead with the cancellation process. Also, add a note that you are planning to close other cards as well.
Even if they give you a meager LE, just initiate the same cancellation process after a month saying that you are not happy with the last LE.
Repeat until Axis finally closes the card.