I've noticed iMessage on my iMac is slow to update sometimes. For example, I sent a message this morning and wondered why the person didn't reply, I looked at my phone 40 minutes later and found she replied a few minutes after I sent it. And then before I started typing this, I sent someone a message and didn't see a reply until I looked at my phone 15 minutes later. But... we've been texting and it's mostly been keeping up. I haven't found a pattern for when it lags. Sometimes it does and sometimes it doesn't. I've noticed this happening over the last few weeks. It was fine before that.