When I try to install SP2 (or simply "repair" the SQL Server installation), the dependency check finds the following problem:
Rule "Not clustered or the cluster service is up and online." failed. The machine is clustered, but the cluster is not online or cannot be accessed from one of its nodes. To continue determine why the cluster is not online and rerun setup instead of rerunning the rule since the rule can no longer detect a cluster environment correctly.
Now indeed the server is part of a two-node cluster. But the cluster is working and this happens whether my server is the active or the passive node and whether cluster services are running or not.