I had trouble once where the American Airlines app updated overnight, and the new version would crash a few seconds after loading. I got around this by taking a screenshot of the boarding pass and showing that instead of the app itself when boarding (I did not have time to go back to the kiosk to print a physical pass). The barcode matched, and I sailed through without any issues.
It is your responsibility to ensure that the mobile phone is sufficiently charged and functional to clearly display the ticket as required for the duration of your journey. If you are unable to display your mobile ticket, you will be required to purchase a new fare (surcharge may apply).
This is repeated in the FAQ:
Q: What happens if my mobile device battery dies before I am able to display my mobile ticket to the conductor/operator?
A: It is your responsibility to have a charged and operational phone so that you are able to display your mobile ticket. If you are unable to display your mobile ticket, you will have to buy a ticket from a ticket agent, TVM or conductor/driver (on-board surcharge may apply).
Note that not only do you need a charged phone, you need an active Internet connection to be able to activate tickets and passes, and that can be difficult if you are underground or in places like the Port Authority Bus Terminal that have overloaded networks. (Once the monthly pass is activated, you no longer need an Internet connection to load it.)
If you are that concerned about the reliability of your device, the short answer is don't buy your pass with myTix. You have no recourse for any kind of technical problems, and both the iOS and Android versions of the NJ Transit app have fairly dismal reviews in their respective app stores.
This is a price you pay for the convenience, but on the flip side, consider that if your phone is broken, lost, or stolen, you can recover the pass on a new device, whereas losing a physical pass would mean you'd need to purchase a brand new one.