Kendra Little explains a problem:
If you use readable secondaries in Availability Groups or Read-Scale out instances in Azure SQL Managed Instance, you may have queries fail repeatedly if there is a glitch and statistics are not successfully “refreshed” on the secondary replica. Those queries may keep failing until you manually intervene.
This has been the case for a few years, and it’s unclear if Microsoft will fix this. There is a well established support deflection article which documents the issue and provides ‘workarounds’.
Read on for Kendra’s thoughts. I haven’t run into this before, myself, but I also don’t tend to make very heavy use of readable secondaries.