This happens to me on Android 4.0.3, does anyone have any recommendations?
Well, I can recommend that you turn off Javascript in your browser of choice... as some webpages have automatic reloading coded on them, that forces the browser to refresh after a timed interval.
If your browser settings happens to have a "reload pages on timer" setting, turn that setting off. Not all browsers have this setting however.
Both the settings above do not account to page rendering which almost happens with most browsers when switching between a page to another in the same app... they only affect the reloading of the page for fresh content.
If your browser supports it, use "save pages option", the page will be saved to disk minimizing the need to reload online.
If you got task managers, set an exclusion to your browser to avoid the browser being terminated automatically. This ensures that your browser doesn't get terminated prematurely, forcing a reload of pages once the browsers are re-launched. If your task manager support OOM value modification, have your browser's OOM value set low - this makes the app the last app that android memory manager needs to kill in order to allocate memory to other applications... eventually android will terminate the app, you're just ensuring it stays alive longer than usual. Task managers like Autokiller can change the values, but its not permanent as Android's built-in memory manager will eventually override the OOM values based on need.