I don't know him or you or what your friendship is like, but consider this - do you need replies?
My current fiance is quite terrible at keeping in contact, it doesn't mean he's not interested or his love for me is any less deep - he just doesn't message people much. We used to be long distance, although we spent a large portion of our time together because we were constantly traveling back and forth. When together, we were inseparable, and when apart - he would sometimes not message me much/at all but I knew it didn't mean anything. He didn't even have a heavy job either! I would still message him, all the time, telling him little things I thought were funny or interesting or that he'd like, or just about my day. I knew he'd read them as and whenever he'd read them, and he mostly wouldn't reply, but I personally didn't need him to. I just knew he enjoyed it anyway and I liked feeling connected to him that way. Now we live together and work at the same place, if we could we would literally spend 24/7 together and never get fed up.
Maybe you could just say to him that you understand he's busy so he can't reply much - but you're going to message him anyway not expecting him to and hope he doesn't mind. If you think that could be enough to keep it alive for you too, that is.
What's your long term plan? Obviously endless messages with no reply are not that much of a friendship, but I imagine you'll see each other again one day too?