Boot loop when discharged after battery replacement

I bought a battery replacement pack for my iPhone 5s from iFixit. Previous issue with the original battery was that the phone was turning off at 20-30% when not in power saving mode.

Replacement went well and I performed the battery calibration. However, when the phone runs out of battery it turns off (no "thinking circle" you usually get). Then it tries to turn itself on again and turns straight back off before reaching the locked screen (boot loop). It does not stop doing this and it happens at random intervals and the apple logo on white background remains on also for a random amount of time each time (0.1s (so fast, not even the whole screen turns on) - 3s aprox).

This has happened from the first time the phone run out of power with the new battery.

To stop the loop I have tried pressing every button individually for short and long periods and tried the hard reboot combination. None of these have yielded results.

I have let this go on for as much as 10 minutes before plugging in to the charger, which immediately makes it boot normally, although it may turn off after it reaches the locked screen and do that once or twice.

On plugging back in the battery indicator reads 1%.

With the new battery I have never seen the "needs plugging in" or the "charging" (whilst off) logos.

Is this due to a faulty battery or some other issue?

Thanks for the answers!