I would check the power supply first as they do all sorts of weird things if they are not happy with it. It's not a bad idea to add a decent sized smoothing capacitor across the power feed to them.
Okay, what kind of capacitor should I put in place ?
I myself, had the same idea, that there is an issue with the p-supply. I ran the ESP-CAM, with an Arduino 5V pin. Maybe as u said, a capacitor ? which one ? Electrolytic ?