If the receiver blocks you on their phone the messages are still delivered, just they are binned without the receiver being notified of them. So that would not explain what you see. Nor would the phone being off - messages are stored in the network's systems until they turn the phone back on, when they are delivered (there is a time-out, but it's usually 2 weeks).
So the most likely explanations are that there is a problem with one of the networks (yours, theirs, or the interface between the two) or that particular number (the number is entered wrongly, or the number has been taken out of service for some reason). You could try phoning the person to tell them that you are having trouble texting them - that would tell you whether the number is correct and the phone account is still active, which would then narrow it down to a texting problem.
