What sort of changes are you thinking of making? I ask more out of curiosity than anything else, since I doubt there are many non-content changes you could do that are likely to harm rankings (unless you change URLs or break something).
To my knowledge Google does not really have a model of pages that "should be static". Similar sites I've had that have not changed fundamentally for several years, but have gone through various iterations of changed links/templates/css etc. have never experienced any problems. There's certainly no "penalty" for doing so, anyway.
Don't make changes for Google, if the site is truly a finished product then leave it that way. People are so bent out of shape trying to please Google that I can't even begin to fathom how many creative hours are lost to the process.
Are you sure it's complete though? Some possible improvements...
- Schema markup ? - Properly minimized and cached? - A CDN if traffic is from more than one country? - Reduced code bloat, combined css/js, optimized database etc?
Any improvement you can make to speed is one worth doing. Otherwise, no touchy. Google is just a ranking service so let them improve their own product.
Wasn't there a recent thread that asked the opposite question? g### seemed to be perfectly happy with old pages, and then the owner made some tiny change and everything tanked :( Made me wonder if something triggered a "re-index from scratch" command in google's innards.
Can g### tell if a page has really changed? The mere act of re-uploading the same files will create a new header with a new timestamp. Is the date of a php page the date the files were first uploaded, or the date the page was created (i.e. right this instant)?
There's no such thing as "should be static". I've got a static site I haven't added or changed anything to in 3 years. It doesn't need to be updated, it's still relevant. I suppose I probably should add to it but that's also not necessary.
Don't do anything for Google, only do for users. If it ain't broke, don't fix it.
There is an idea out there that 'google wants things to change', so people make changes to their page that are meaningless, for want of a better term - they just switch up the content. They are missing the point of "Google wants change" - here's a comparison: Tom overhears Bob talking about how much money he has made buying and selling stocks and shares. Tom thinks about this and reasons that all Bob is doing is moving money around, so he starts regularly swapping $100 between 2 cheque accounts, sure that this will make him more money than if he just left it alone. Tom has missed the point - the point wasn't just to move the money around, the point was to move it from the wrong place to the right place. Likewise in websites - if you do something to improve your website then it will increase in value. If you just reshuffle things, you have wasted your time. :)
The question I would be asking myself in such a situation is not whether or not I should be doing updates for Google, but am I still the definitive authority on this topic, without adding anything to the site? In other words, I'd be looking at my competitors, not to Google.
That made me realize the one thing you do need to change periodically. Even if you've written the Article For The Ages, the sites you've linked to may not be as obliging. Check the links physically now and then. That is, with your eyeballs, not just a tool. It isn't enough to verify that the links still work. You need to make sure the stuff at the other end is still something you want to be associated with.