What is wrong with the arch of my foot? It goes down when I stand up?

Flat foot Pes Planus. Pes planus or 'flat foot' is a very common condition in which the foot does not have a normal arch when standing. Weight gain, aging, injuries, or illness may harm the tendons and cause flat foot (or feet) to develop in a person who has already formed arches. Treatment includes 'arch support' or orthotics (over-the-counter or custom made). A 'podiatrist' (foot doctor) may help good luck.
Flatfoot. That is a common response to weight bearing . However, if excessive, it may lead to symptoms. You may first try an otc arch support , but if symptoms persist you should seek professional care.
Weak arch. Ligament on plantar surface is weak, flat feet, need arch support, ie. Othotics.
Flat Foot, Pronation. This is probably a classic flat foot deformity or sever pronation of the subtalar joint. Different foot orthotics, braces or shoe modifications can be tried first. If conservative care is not adequate then surgery is available.
It is flexible. It sounds as though you may have a flexible flatfoot. It should be examined to check the extent of the problem and to see how to stabilize it.