Quotly registers its emails with WooCommerce, so you edit them under WooCommerce, then Settings, then Emails, next to your order emails. Look for the entries starting with Quotly.
Subject lines, headings, and the wording are all editable, and they use your WooCommerce email header, footer, and colours, so they match your order emails without extra work.
A reminder before a quote expires, an expired notice, and the two message thread emails.
This is almost always the host, not the plugin. If your WooCommerce order emails also fail to arrive, install an SMTP plugin and send through a real mail service.