[V2] UPS powering off prematurely when on battery

[misch2]

Step up module: https://www.aliexpress.com/item/1005004596697480.html

Its description says "2-24v to 3-30v 4A 80w CC CV".

On a lab bench supply it was able to produce 12 V / 3 A from 6.8 V input.

When used in UPS and powered from Li-Ion 3000 mAh battries the results are:

Output current	Output voltage	Battery current	Battery voltage
0.01 A	12 V	-	-
0.5 A	11.68 V	-0.86 A	7.78 V
1.0 A	11.45 V	-1.83 A	7.5 V
1.5 A	11.33 V	-2.95 A	7.15 V
2.0 A	11.15 V	-4.22 A	6.78 V
2.5 A	11.04 V	-5.76 A	6.42 V
2.9 A	10.99 V	-7.86 A	5.8 V
3 A	-	it turns off	(even when I add a capacitor to the output)