There are different types of SZ…some show “positive” effects (hallucinations, delusions), others are “negative” (withdrawn, apathy, lack of speech). And the effects can come and go. I agree that texting every few days (or whatever you consider to be enough but not obnoxious to a person who is not able to respond quickly or at all) is a good idea.
Our son, who had more “negative” symptoms of SZ, went missing suddenly and for 3 months and we knew his general whereabouts while he roamed and lived out of a car in a far away state but could not really make contact with him. So we kept texting, not knowing for sure what or if he was reading. During that entire time, our son texted me back ONE time. That one response was so precious to me. In fact, I just showed that text to him today! He remembers very little of that time, but is doing MUCH better now!
He still reads emails rarely and has not been on Facebook in years. But he HAS started reaching out to friends, which is huge, and he talks with other people.