Answer
Check whether the cluster's DNS was configured with the installer's dedicated DNS-setup step during initial middle-tier setup — without it, pods fall back to default public DNS servers (which genuinely can't resolve internal-only hostnames) instead of consistently using your internal DNS server, producing exactly this kind of intermittent, coinflip-style resolution behavior. Running the installer's cluster-DNS-configuration resource step (main.ps1 -resource 'SETK8SDNS') points the cluster's internal DNS correctly and resolves this.