I have the same problem. There seems to be an issue between Android/HTC One and certain iPhones. I notice two issues.
INDIVIDUAL MESSAGES: There are some iPhone users that I communicate with where everything works just fine. Other times, receiving 1-1 messages, ocassionally certain iPhone messages come thru to me only as a message header 'from, subject, date, time,' etc, and the word "download" and an arrow graphic. I click these but the messages never download.
GROUP MESSAGES: There are some iPhone users who can text to me within in Group thread, but my replies are received as blanks messages on their end. I can send individual messages to certain members of the group and those messages work fine. Troubleshooting this issues, I started a new thread with the same people to see what would happen, and messages are sent as blanks once again. NOTE: What's most maddening about this is that at one time I could communicate in group threads with all these same iPhone users, suddenly now I can't.
Anyone have any ideas?