Is there a way to continuously monitor the status of relational database connect

I am not sure I would recommend doing this is Appian. You could, but there are tools specific for this kind of activity. If you wanted to do this in Appian, you could have a model run on a timer and have a Query RDBMS node to 'select 1 from dual' or something like that.

That is pretty much what we did, we have a process that attempts to query the DB every 10 minutes and will send an alert and email on failure.

Thank you.

You may try configuring Introscope powerpack to monitor the DB and server statuses which is used in most of the orgs