I wonder if other family members have asked this individual to keep close contact with you because you have altered the parent texting? No matter, here's what you do.

I strongly suggest not replying right away or, if you do, text back "I can't respond right now as I'm working/at the store/on the phone/tied up/with a friend". You get the picture. The quick "can't reply right now" will get them off the panic button. It also discourages numerous texts because they will get tired of waiting a day or two for your response. Make sure you wait a full day or more and if you get flack tell them you were just so busy and replied as soon as you could. That should do it.