Magento has default feature to keep the user logged in to a particular browser and for custom design it may not be visible .
Add the following to custom module layout to
Magento Customer>layout>customer_account_login.xml and customer_account_create.xml
<referenceContainer name="form.additional.info">
<block class="Magento\Persistent\Block\Form\Remember" name="persistent.remember.me" template="Magento_Persistent::remember_me.phtml" before="-"/>
</referenceContainer>
Turn on the persistence option in back end.