Actually, the browser component is not destroyed, but it seems to be hidden from container and inaccessible, so in order to workaround I followed this steps to kinda keep it.
Before changing BorderStyle, first set ActiveXContainer.Active to False, then change BorderStyle, afterwards restore ActiveXContainer.Active to True, but it will be shown a blank content, so Navigate2 is called again (the page will be loaded again), which is not what is expected. But at least is better than having browser lost.
Hope someone shows the correct way to fix this issue.