If buyer request is closed by fiverr due to low ranking should we maintain our account or remove and make a new account for buyer request and start working?
No. If you read how Buyer Requests work you’ll see you only get access to a couple if you are a new seller.
Isn’t it easier to research how things work?
Though the OP is saying he gets access to none at all (eg. because of his average rating). It doesn’t let you access it/send offers unless you are at least 90% positive rating (I think that means at least 4.5 star average), which means just one 4-star review at the start can mean you can no longer send offers to BR.
Maybe if it’s been a long time since you got an order and BR is the only way you’d have really of getting an order, you could ask for permission from Fiverr/CS to close the account and open a new one (which would then allow access/sending offers to BR).