Static homepage and SERP

I find Google does give more weight to sites that are consistently updated.

@ Sezerb

Google indexes sites more often when they know content is added regularly but as for ranking them higher in the serps, this would only happen as google see's fresh content and ranks it well for a week or so then the new content would drop down some.

To answer the question though:

@ Can not having a static homepage hurt your SERP?

Yes and no ;-) You may find some variations in your rankings when adding fresh content to the homepage as your keyword density for your desired keyphrases changes. However, if you make sure your browser title, H1 and initial paragraph are static then as this is what Google looks at first (high up the source code) then you should be OK. If you also have a good amount of one way links for your desired keyphrases then this will help your rankings be more stable.

@ but time to time it just disappears completely or it just drops out of the rank so far down that I can't even find it within top 20pages.

Sounds like the Google dance to me, which happens even more with new sites. Even my established site sometimes drops off the radar when Google does an update, going from #1 in Google to #11 and back again multiple times over a few days. I really would not worry about this too much unless of course it turns permanent, then you know you have more SEO work to do in the way of links and page content.

New content is a good thing, and assuming the content is indexed and stays within your site it adds more keyphrases for people to find you by so you are doing the right thing. However I would change one lil thing on your homepage, at the top you have some static text " Learn to give up smoking from someone who's done it" with a lot of white space below it, this is your perfect place to have some static content so if I was you i would pad that our with a few more keyword rich sentences and perhaps stick a header 1 tag in there also.