I run an AR at the end of every month, and follow up with any claim that is over 30 days. Most payers pay clean claims within 10-21 days, and if it hits 31 days, I know something is potentially wrong.
As EOB's come in during the month, and if something should deny, I follow those denials up immediately, same day or next day at the latest.
I don't ever "routinely" check claim status, though, like you mention doing. So long as my clearinghouse reports show that the claim was accepted for processing, that is good enough for me until a denial comes or no response after 31 days happens.