This is an interesting question. The Doctor's Tardis is a Type 40 which was an antique even before he stole it. We do not know it's exact age but it certainly is ancient. As we know, it has a faulty chameleon circuit and is constantly being repaired by The Doctor so there is definitely evidence that a Tardis breaks down over the centuries. In the 2006 Tenth Doctor story, "Rise of the Cybermen", the Tardis completely breaks down and is only restored when The Doctor sacrifices some of his future years to a remaining power cell that is just clinging to life. In the 2013 Eleventh Doctor story, "The Name of The Doctor", The Doctor travels to his own grave in the far future. Instead of a headstone, there appears to be a huge monument of the exterior of the Tardis. The Doctor explains that this is in fact the actual Tardis which has broken down and "all the bigger-on-the-inside starts leaking to the outside".

So in conclusion, Tardises do eventually break down and perhaps The Doctor's would have broken down earlier if he wasn't making constant repairs!

The TARDIS has a living consciousness. It has a "Soul". So, maybe, when the time comes... she may die. However the fact that they are also Gallifreyan could mean they are essentially immortal.

Plus the Doctor's TARDIS is a beast. She can survive anything!

It's like the explanation of how it works. Some parts of the script are not explained but left to the imagination, usually because there isn't a rational explanation to give. Just enjoy the show, and wait for the final episode.

no

How does a TARDIS die? Since they're grown do they die old age or something or do they just break down like a car? I was just wondering since I'm not sure if they've mentioned it the show, have they referenced it at all?