Emil, man I totally agree!
We do monitor all our servers and database servers all the time, so many times when a 'db connection' error pops up, and it's not due to an outage, we don't see anything 'wrong' (realistically, you might be working on things, or editing your PHP, or messing with your VPS). If the server is down, you bet your bippy we're on it like Chuck Norris. But when it's something else, it's hard to say.
For people running into this for the first time, there are (sadly) a lot of reasons you can get that error.
The very first thing to do is make sure the DB is up! You can go to myql.domain.com, and log in with the password/user combo in that wp-config.php
Assuming you can log in and all your data is there (remember to match your WP prefix to the table names you see), check if you made any PHP changes (like to php.ini or phprc). It's really easy to shoot yourself in the foot with that (please don't ask how many times I have ;) ).
If you didn't make any changes, tell us! In fact, telling us what you already tested saves us worlds of time, and helps us get through even more tickets. Part of the reason we can't answer everything as fast as we want is that we have to go back and figure out what you may or may not have done. Giving support the right amount of info to skip steps is hard to learn, but as you do, you'll find we can fix things faster and faster :)