At some point, a customer originally targeted may not be profitable to serve. Thoughts?

Sometimes the hardest thing for some marketers is to say “You are not my customer”.   In reality though, you are trained as a marketer to segment, segment, segment, and target.  So, your best decisions are driven around who your customers are, thus defining who your customer is not. This is much more clear in B2B marketing, versus B2C marketing.  At some point, a customer originally targeted may not be profitable to serve. Thoughts?