WordPress server banning IP

I am getting a weird problem with a client site. There is an existing WordPress working on it and has been working without any problem.

I have deployed a mobile application that uses the WordPress API.

Suppose my laptop and mobile app is connected to the same Internet Box. When using the mobile app, after I am unable to access the website even with my laptop. It seems as if the WordPress server or WordPress instance is banning my IP.

To be able to use access the site, I have to restart my Internet Box, after which it gets a new public IP, it is only then I am able to access the WordPress site.

I am suspecting where there is an option somewhere which bans an IP if it requests too much data.

Any suggestion to solve this problem?