I think you're making overmuch of the word "chase", I can substitute it for "follow-up" if you wish. I messaged my teacher infrequently to ask a question and would not receive a reply for about two to three weeks on several occasions - often I could see that they had read the messages too. I don't believe that that's an appropriate amount of time to leave a message from a student. At no point did they tell me that they were too busy to reply to messages, or apologise for the delays, in which case I would have understood. —
Lou 1 min ago