1. A computing system, comprising: a plurality of computing nodes, each of which comprises at least one processor and a memory; wherein one or more reserved resource instances executing on the plurality of computing nodes implement a database service, and wherein the database service comprises a database engine head node and two or more server nodes of a distributed storage service that stores portions of database tables as respective data pages on one or more storage devices; wherein one or more other resource instances in a resource instance pool are designated as contingency resource instances for the database service, but are not reserved for the exclusive use of the database service; wherein, while the database engine head node is operating as expected: the database engine head node is configured to: receive, from a client of the database service, one or more write requests, each directed to a respective data record in a database table and specifying a modification to be made to the respective data record; and route information about the specified modifications to particular ones of the server nodes of the distributed storage service; the server nodes of the distributed storage service are configured to: apply the specified modifications; and a resource management component executing on one of the computing nodes is configured to lease one or more of the contingency resource instances to a client under a spot market model, wherein leases for the contingency resource instances are revocable by the resource management component when they are needed for the use of the database service; and wherein, in response to determining that the database engine head node is no longer operating as expected, the resource management component is configured to: revoke a lease for at least one of the one or more contingency resource instances; reserve the at least one of the contingency resource instances for the exclusive use of the database service; and instantiate another database engine head node using the at least one of the contingency resource instances.