The current document is directed to methods and systems that efficiently cache log/event messages in log/event-message systems incorporated within distributed computer facilities. The log/event-message systems provide the data-collection, data-storage, and data-querying functionalities that provide a basis for distributed log-analytics systems which, in turn, provide a basis for automated and semi-automated system-administration-and-management systems. Efficient caching significantly extends the period of time that networking failures and log/event-message processing delays can be tolerated by log/event-message systems without significant loss of information. Rather than caching individual log/event messages, message collectors that employ the currently disclosed technologies cache information regarding log/event-message types, leading to efficient compression of the cached information. As a result, message collectors can cache log/event messages without significant loss of information for time periods of several orders of magnitude greater than those achieved by caching individual log/event messages.