I think there is a certain danger of that happening, but we would have to specify it further; citing sales numbers or mobile browsing shares isn't enough. Ultimately, it comes down to the different user experiences offered by the two operating systems. Since Apple traditionally places a lot of emphasis on smooth, refined and simple interfaces and a good feature set, one would instinctively assume that they don't have much to fear. There are a few surprising advantages to Android though, which I detailed in a different post. Allow me to quote myself:
I recently got a used Nexus 4 out of curiosity. I'm using it as a secondary device next to my 4S and it's been a pretty interesting experience. There's a lot I could say about the differences between the two phones, but the main point for me that really makes me love the Nexus and think of the iPhone as slightly antiquated is the basic home screen concept. Apple's app-centric and mostly static home screen (or Springboard, if you will) was awesome in 2007 because it was much prettier, easier to use and snappier than the competition's offerings. It became even more awesome in 2008 when Apple introduced the app store and one could easily download and install applications that actually added a ton of value to the device. I'd had a smartphone before the iPhone came out, but I never bothered installing 3rd party apps - too complicated, often didn't work, added little value... etc.
However, we're all used to our smartphones being awesome little pocket computers now. Personally, I'm getting more and more interested in UI paradigms that aren't app-centric, but information-centric. And that, I think, is by far the most significant difference between iOS and Android ("openness" and "customizability" are important too, but mostly to nerds) and it's the one difference Apple might have to do something about. When I unlock the iPhone, I'm presented with a mostly static app launcher. Springboard offers very little glanceable information: There's the time, the network and battery status, the date, and tiny notification badges on some apps that tell me nothing except that these apps wish to tell me something. I can customize the arrangement of the apps and the background - and that's pretty much it. As soon as I actually want to do something or find out what those notification badges are about, I have to launch an app. Again, this is not a bad design; it's served Apple well and it was revolutionary a few years back. I do think, however, that it's starting to become a bit of a burden. Why can't I customize my home screen to display information that is important TO ME, like, say, the weather, 3-5 unread mails or messages, the next few appointments in my calendar, my twitter feed... Whatever. I can only speak for myself, but having to launch separate apps to glean all of these pieces of information gets old really fast. And it's not just the apps, it's settings too - I have to delve into submenus to toggle Wifi or Bluetooth.
On the Nexus, this plays out in a way that I consider to be more productive and, to be honest, intuitive (ugh, you know something's weird when I consider Android to offer more ease of use than iOS). When I unlock the phone, I'm greeted by a home screen that offers me access to my most used apps (in the dock), to the rest of my apps via the app button, but above all: to a host of glanceable, live-updating information that I can actually customize. I unlock my Nexus and I immediately see widgets displaying my inbox, my calendar and the local weather. If I get bored of these widgets or if I discover that other scraps of information might be more useful to me, I can just replace them.
Apart from all the other relevant distinctions between the two operating systems, apart from all their respective strengths and weaknesses, THIS to me is the key difference - the screen as a personal canvas that displays the information of my choosing (Android) or as a rather rigid app launcher. I'm not saying one is necessarily better than the other; it's a matter of taste. Personally, I prefer the Android paradigm, but I'll still probably sell my Nexus again because I'm just too locked into Apple's ecosystem. I merely wish to point out that this is a very significant factor in these debates about iOS feeling "stale" and that Apple might ultimately have to do something to allow us to really make the home screen our "home". This is not about silly widgets and live wallpapers, it's about empowering the user to actually get the most out of a portable, always-connected device.