Oh Nicholas. Sigh. I'm going to have to agree with most of the answers you're getting, but with a strong caveat due to your specific question...

My clients often work with me for decades/generations! Yes, we absolutely develop on-going relationships, including "friendships". And it's the relationships that make my work so rewarding. But if you're going overboard with your efforts because you've become "emotionally invested", you're going too far! You're setting yourself (and them!) up for disappointment at the least, and devastation at the worst. "Stuff" goes wrong. That's life. If you/they are going to feel a business-problem personally, you'll end up with both relationships suffering. You can LIKE them, but still keep your relationship business-like. You mustn't spend more time/effort than your business can afford...