In LO you could set values for connection pooling: Tools → Options → LibreOffice Base → Connections
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It has nothing to do with holding a connection for example to a MySQL server somewhere in the www. This kind of connections will be limited by the server, not by a driver of LO.
Connection pooling seems to be used in a multi user environment. A connection from one user to the database will be saved for the pooling delay. So another user could use this connection and mustn’t establish a new connection.
I don’t know if I understood it right but I couldn’t find any reason to enable connection pooling. Could be it is impossible to reproduce any difference in behavior of database drivers for a single-user system.
I want to describe this in next Base Handbuch
in German, but the help for this “feature” isn’t very helpful.