First thing to check is that the contact has allow contact by SMS set to yes. To do this go to the student profile, expand the contact and click the cog next to their name.
Then check the permissions at the bottom of the contact screen.
If this is set to no it will need amending to yes and saving if the contact has given permission for this.
If this is already set to yes you may need to check the number. To do this click the cog next to phone numbers. Firstly check the length of the number as sometimes digits can get missed or added. Then check the type; for a number to be used to send an SMS in comms the type needs to be mobile (M). If this is showing as home (H) you will need to amend this.
To amend this click edit, select the type as mobile and save: