How to overcome a glitch in the iPhone 4S with shutdown and inability to start up to discharge?

Question

iPhone

Hello. There is an iPhone 4S, with iOS version 8.4.1, it costs JailBreak. It is used to automate certain actions, and it is always on charge, but in the process of work every 1-2 days there is a glitch:
The network disappears, in the browser: "Safari cannot open the page because the iPhone is not connected to the Internet."
And as soon as I turn off the charger (100% charge), the phone turns off dead. When you try to turn it on: an apple appears, hangs for 5 seconds and the phone is immediately cut down. And so in a circle. If you return to charge - also.
Then I had two outcomes of events:
1. The phone itself lost its charge in 2-5 hours completely, I put it on charge, it turned on and then everything was OK.
2. The phone did not lose its charge, up to 3 days (I did not observe it further, I did the restoration).
Actually, with what there can be a problem and how to overcome? On the one hand, it seems that the battery is to blame, but then why are there problems with the network?
What I have tried and also observed during this state:
1. In the browser "Safari cannot open the page because the iPhone is not connected to the Internet". The apps also don't have a network.
2. Reconnecting Wi-Fi did not help.
3. When you go to the settings, it bugs out: a white screen. After entering the settings in the "Wi-Fi" item, it was displayed: "Not connected". When you click on the wi-fi item, there was a freeze for 15 seconds.
After there was a transition to the wi-fi settings, the phone cannot find other networks (the "select network" hangs and the download spinner).
4. Tried resetting network settings. As a result: a black screen with an apple icon, the progress bar filled up completely, after the loading spinner in the middle of the screen, and the phone seemed to turn off. After the usual glitch with the inclusion.