Is this for a custom domain? With any mail service using a custom domain, you'll need to configure your DNS with SPF and DKIM (and preferably DMARC) to ensure acceptable delivery to the big guys. I can't speak directly to Namecheap, but sending mail from any custom domain without SPF and/or DKIM is going to go poorly these days regardless of host.

If you haven't already done so, read this first: https://www.namecheap.com/support/knowledgebase/article.aspx...

Also potentially: https://www.namecheap.com/support/knowledgebase/article.aspx...