Adwords Quality Score? How Often Is It Updated?

Quality score is calculated every time your keyword is eligible for the auction. This can happen several times a day. Google shows an average of the day.

Here are the factors which influence the QS.

Your keyword's expected clickthrough rate (CTR): The expected CTR is based in part on the keyword's past CTR, or how often that keyword led to clicks on your ad
Your display URL's past CTR: How often you received clicks with your display URL
Your account history: The overall CTR of all the ads and keywords in your account
The quality of your landing page: How relevant, transparent, and easy-to-navigate your page is
Your keyword/ad relevance: How relevant your keyword is to your ads
Your keyword/search relevance: How relevant your keyword is to what a customer searches for
Geographic performance: How successful your account has been in the regions you're targeting
Your ad's performance on a site: How well your ad's been doing on this and similar sites (if you're targeting the Display Network)
Your targeted devices: How well your ads have been performing on different types of devices, like desktops/laptops, mobile devices, and tablets – you get different Quality Scores for different types of devices

You need to optimize everything for a better QS. Good luck!