It can be achieved with the help of an observer.

Follow the below steps to create an extension PHPCodez_Keeplogin for this task.

1) Declare a module.

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:Module/etc/module.xsd">
<module name="PHPCodez_Keeplogin" setup_version="0.0.1" />
</config>

2) Register a module.

<?php
\Magento\Framework\Component\ComponentRegistrar::register(
\Magento\Framework\Component\ComponentRegistrar::MODULE,
'PHPCodez_Keeplogin',
__DIR__
);

3) Create frontend/event.xml file and add the below content.

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:Event/etc/events.xsd">
<event name="controller_action_postdispatch">
<observer name="Keeplogin_controller_action_postdispatch" instance="PHPCodez\Keeplogin\Observer\KeepCustomerLoginObserver" />
</event>
</config>

4) Create an observer KeepCustomerLoginObserver.php

<?php
namespace PHPCodez\Keeplogin\Observer;

use Magento\Framework\Event\ObserverInterface;

class KeepCustomerLoginObserver implements ObserverInterface {

private $customerUrl;
private $context;
private $contextHttp;

public function __construct(
\Magento\Framework\App\Action\Context $context,
\Magento\Framework\App\Http\Context $contextHttp,
\Magento\Customer\Model\Url $customerUrl
) {
$this->context = $context;
$this->customerUrl = $customerUrl;
$this->contextHttp = $contextHttp;
}


public function execute(\Magento\Framework\Event\Observer $observer) {

$controller_name = $this->context->getRequest()->getControllerName();
$action_name = $this->context->getRequest()->getActionName();

$isLoggedIn = $this->contextHttp->getValue(\Magento\Customer\Model\Context::CONTEXT_AUTH);

if ($isLoggedIn) {
return $this;
}

if ($controller_name === 'account' && ($action_name === 'login' || $action_name === 'loginPost' || $action_name === 'forgotpassword'
|| $action_name === 'createpassword' || $action_name === 'create' )
) {
return $this;
}

$customer_login_url = $this->customerUrl->getLoginUrl();
$this->context->getResponse()->setRedirect($customer_login_url);

}
}

5) Issue the following commands.

$ php bin/magento indexer:reindex
$ php bin/magento setup:upgrade
$ php bin/magento setup:di:compile
$ php bin/magento setup:static-content:deploy -f
$ php bin/magento cache:flush