RBL is very clever, they are not going to reply to your email, they only give call back from a mumbai landline number.
I also faced one issue I m using RBL V card since last 4 years with annual membership fees, this card had a feature to transfer the limit to upi n take loan of the card limit, these features are now permanently closed
I escalated to pno for any other variant of card, they rejected my request saying they don't have any offers
But RBL is very generous in credit limit increase they always increase more than 70-80k limit per year this year they increased it 55k
I have more than 11 bank credit cards. As of now only RBL n one card is increasing credit limit with any documentation
All others have stopped even sbi has enabled a mechanism it's going to check your bank account balance to decide
My suggestion will be try for RBL co branded cards, you need to be very patient now days for credit limit increase.
Hdfc made the credit limit double after 4 years
N also you need to be very careful with your choice of words while speaking with customer care don't say that if the limit is not increased I will close the card, the executive will take a request immediately.
You can tag their social media channel like twitter they will only give call back n specify the reason
But the first priority should be to make the payment of the dues
All of the above is my personal opinion