Laravel API Becoming Unresponsive

I have testing environment for a new project in AWS. The backend API is developed using Laravel v6 and frontend in Angular. The API sits behind load balancer. When we do load testing with limited number of multiple concurrent requests, initial few requests gives response immediatly, however after 20-30 request the laravel server becomes unresponsive. As we checked the log files, there is no information available for that particular duration which implies that web server could not reach laravel API and then request gets timeout.

Testing approach -

1. First we tested using Jmeter -> same result
2. Then we tested manually with 10 member testing concurrently in 20 sessions -> same result
3. Even we tested API by directly hitting through Postman -> same result

The API project reads/write to DB, encrypt/decrypt some fields, generates couple of reports and uses few AWS services. Issue with db query seems little implausible as same API end-point gives fast response in initial request and becomes unresponsive when testing continues.

lsof command on laravel port shows 2-3 session when response time is fast, when API becomes unresponsive lsof will show 40-50 session.

Thanks in advance for any guidance.