Checking the Netweaver docu e.g. here (Creating a DBCON Entry - SAP NetWeaver Technical Operations Manual - SAP Library) helps with this!
There is a checkbox to indicate that you want the connection to be open permanently.
The re-open time you see in the trace however is not related to the db connection but to the DB cursor. So unless you find that creating the connection actually is the problem here, setting it to permanently open might not solve your issue.