Then it is nothing at your end. I think that this other person's phone is having the issues.
Check with the person to see if s/he has this issue with only you or with everyone else.
If everyone else then s/he has to go SETTINGS, then GENERAL and then MESSAGES.
Ensure that iMessages is turned ON and activated. Also under SMS/MMS the MMS should be ON.
Also if s/he is having same issues with everyone else then s/he will need to bring this up with the cell phone service provider.