I think it's not a question of style or Perl, it's a question of: What is your programm supposed to do?

Is it a general tool for monitoring databases?
Then you should probably put all the configuration stuff into a separate file or some separate files and your program should retrieve the connection information from there.

That way you can easily add new databases or change existing ones without touching your program.

Is the main purpose something else and you have check upfront whether the given 2 databases work, I would use a loop if the tests are identical. If the tests are not identical, I'd use two connections tests (and descriptive names).