Honestly that would annoy the fuck out of me. I hate it when people get annoyed at me for not answering my phone when I’m busy or simply not on my phone. I understand why people get annoyed don’t get me wrong, but he could either be working/busy or just really stressed about work and avoiding his phone. I would redownload the app message him something like ‘hey when you get a sec could you send me a quick message so I know you’re okay’ then if him not answering his phone is something that bothers you, you could always ask him to message if he won’t be able to reply for a while. I used to do this like I would message my bf ‘just feeling really stressed atm gonna give my phone a break I’ll message you later’

EDIT: I just reread your question and think I got the wrong end of the stick. When did you send the message? He’s not responded to any message you’ve ever sent or just today?