I have worked with a lot of the 'jailbreakey types' (they worked as security researchers / white hat hacking if you will). Almost as the above poster said, to find the type of hardware and software exploits, you require considerable access to the device and heavily rely on keystroke combinations (like that required to enter DFU mode on an iOS device) to force the exploits to run or to provide a methodology to perform the exploit. The earlier post detailing software issues is semi-inaccurate in that the version of iOS powering the Apple TV second and third generations is actually incredibly similar to that used on iOS 'proper' devices.
The problems with the Apple TV 3 are twofold
1. Although they run a very similar OS, the version of iOS running on the Apple TV 3 & 2 could be said to be in 'kiosk mode' - although many of the software exploits are in fact present in the production OS, the OS is so locked down that there is no way to exploit the vulnerabilities that exist. The hardware buttons and many software features that would be helpful in crafting an exploit although present are totally inaccessible to the user.
2. The Apple TV 2 as previously noted was only exploited due to it using exactly the same A4 chip as was present in the other devices of its time and this chip also happening to have an easily exploitable hardware vulnerability. The Apple TV 3 is unique in that it is the only iOS device (in the Ax Chip era) to use a chip not present in any other device meaning that even if a hardware exploit was found on another iOS device using an equivilent generation chip, the chips are not sufficiently similar for that exploit to be easily 'ported' to the Apple TV, a process made only more difficult by the fact that the OS powering the device is so far locked down that discovering the vulnerabilities that are almost certainly present in the devices hardware and or code is nearly impossible.
A lot of parallels can be drawn between this example and the case that many ATMs can run very securely on decades old software riddled with vulnerabilities simply because the user facing portion of the software is so well and so completely locked down that exploiting anything is near on impossible. Of course, this is only possible on devices like the Apple TV 3 because the manufacturer controls literally every aspect of the software - this would never be possible on iOS proper because every single developer would have to approach apple to make their app alongside them etc etc etc.
Even apps like PlexConnect that 'exploit' the system do not really - they really exploit Apple's somewhat flawed implementation of content delivery - in short they only manipulate already existing tools and features. If there is any exploit at all taking place, it is no more than 'skin deep'. Again, these are only possible because of how easy it is to monitor network traffic.
I think we'll see a Jailbreak for tvOS long before a workable jailbreak for the ATV 3 although now that it is edging into obsolescence we may see a jailbreak emerge if exploits are found in the methods apple has used to lock the system down due to bugs (like 'heartbleed' emerging) that apply to any and all software using the code.
Sorry to drag this up again, I just wanted to provide a better answer for anyone still curious. Feel free to comment if anything I have said is wrong / inaccurate. Hope y'all enjoyed getting the notification etc
tl;dr exploits are only discoverable on an OS that isn't totally locked down, the very nature of the Apple TV OS of the time prevents searching for the flaws. This is only hindered further by the uniqueness of the A5 chip found in the product.