any tips to maintain the google PR that we've got on an update? What will happen if we do nothing to promote the site? Will the PR go down next time?
Although it feels good to have good PR, it has only a small effect on your site's rank positions. It is a waste of time to dwell upon it unless you are using it to sell links.
With the last update, the PR went down on my most popular sites, but is did not affect their rank positions or the flow of traffic, which continues to improve.
PR is simply the value that Google places on the links pointing to a web page.
"Democracy is two wolves and a lamb voting on what to have for lunch. Liberty is a well-armed lamb contesting the vote." -- Benjamin Franklin
In order to answer your question, just keep backlinks coming into your site from high-PR websites. Your site gets its rank from other sites giving you PR-juice, so keep posting on forums with your signature links and keep leaving blog comments to bring backlinks. Over time you may even raise your PR, but it will definitely stay the same with some basic backlink maintenance.
maintaining backlinks count or adding will probably will keep your PR.
I still have a small website on 110mb.com the VideoScreenSaver for a screen saver that I made. I just updated it couple of times to add more links on it, but didn't make any new backlinks. It has PR3 since 2007