Automate the update, not the apology
Status updates are a great thing to automate. Clients like knowing where things stand, and a scheduled update covers that need without you writing the same message by hand every time. But apologies, explanations for delays, and anything needing context should stay personal.
The line between the two is simple. I've caught myself trying to automate an apology before, and it read as cold every time. An update reports a fact: here's where things are. An apology explains a problem and asks for patience. The second kind needs a real voice behind it, because it's carrying more weight than a plain status line ever will.
If your automated update system ever needs to explain a delay, pull that particular message out of the automatic flow and write it yourself. It's a small extra step that protects the relationship far more than it costs you in time.
Try this today: look at your last few automated update messages and flag any that were actually covering for a delay. Rewrite those by hand instead of letting the template carry them.