So, I thought I had a simple explanation of how all this works, but first I experimented a bit and got totally confused! This is what I found. It will probably unnecessarily confuse you even more and it's way too long of a description of what I found, and it probably doesn't answer your question, but here you go!
If you tap the persistent search bar on the home screen, or swipe up from the home button, Google Now appears. If you tap the persistent search bar, your cursor is already in the search box when Google Now appears, and your keyboard pops up. If you swipe up from the home button, the nice stylized Google Now background appears, but you have to tap inside the search box to activate the keyboard, at which time the background slides away. Either way, you end up starting your search at the same place.
You then type your search query. You can also say "Google" or tap the microphone icon in the search box, and speak your search query. Either way, the same thing will happen as described next. Google Now does the search and shows results. When you choose a result, the Chrome (or default) browser opens to show you that website. If you press the bottom back button (not the back button in Chrome), you'll go back to the Google Now search results. Press it again and you'll go back to Google Now. But if you open another app first or even open the recent apps list for a second, then pressing the back button brings you to the home screen. However, you can then simply tap the recent apps button and choose the Google app to bring up your search results again. Easy enough, I suppose.
But what if you want to skip Google Now altogether (or at least not see the Google Now cards)? Simply tap the microphone icon in the persistent search bar, and the Google "speak now" box appears. Say your query and the search results will pop up. Almost everything then happens normally, like above, except for the problem you described.
Oddly, if you go to the home screen right after bringing up the website from your microphone-only query (made directly from the persistent search bar), the search results are no longer available in the recent apps list. Sometimes Google Now or the search results also disappear from the recent apps list after searching via Google Now, but it's not as immediate as doing a microphone-only search. Additionally, if you do lose your search results after the microphone-only search, it seems your query doesn't appear in the search history list when you initiate a new Google Now search. I'm not sure what triggers this, but it is a bit annoying. I think this is just an Android and Google Now oddity, and will probably be improved in upcoming releases.
Perhaps the easiest thing to do in terms of getting back to your search results is to just skip searching via Google Now or the persistent search bar. Instead, open up Chrome and search directly from the search/address bar in the browser. Then you can navigate back and forth between the results and the chosen websites, using the Chrome back and forward buttons. Or long press on a website search result to bring up the option to open that site in another tab, which leaves your search results tab readily available.
This is kind of unrelated, but if you want to get rid of the persistent search bar, install an alternate launcher that lets you remove it. Nova Launcher Prime, which I use, lets you do this. It's nice to have the extra space. If you still want a search bar on one of your home screens, just place the Google Search widget there.
I hope this overly long response was of some assistance. I now have to take a shower and get ready to watch the 49ers trounce those wicked Ravens in the Super Bowl! Go Niners!!
EDIT: Niners lost. I'm depressed. I vow to never watch another 49ers game until September. Go SF Giants!