Messages typically fail for one of two reasons.
The first is that the contact has changed cell phone providers, but keeping the same mobile number. (For example, switching from Verizon to T-Mobile but taking their number from one provider to the next.) This failure is simple to fix:
1. In the left menu bar of your workstation, click on Search Contacts
2. Search by first name, last name, or mobile number
3. Click the Edit Icon once you find them
4. Click the "Update Carrier" button to the right of the cell number
If the cell carrier doesn't change, this contact may have a short code block on their phone. It's not very common, but luckily it's an easy fix. The contact simply needs to dial 611 on their cell phone. This will call THEIR cell phone provider's support line where they can ask to have the short code block removed. It typically takes a couple minutes and you will be able to successfully send messages to their phone.