Let's Encrypt goes down, certs can't be renewed, people can't access websites securely (or at all if HSTS was used).
It's unlikely they would be down for so long that certs would actually expire.
Just pick a discrete number of days before expiration such that you have a comfortable amount of time to deal with issues.
We (Let's Encrypt) recommend renewing with 30 days left, so every 60 days. If your system is automated like we recommend that shouldn't be burdensome, no reason to do it less often than that.
I can see pros/cons either way, just thought you might be interested in this feedback.
Having more options means less fallout if a CA gets compromised.