Bicycle tires will lose pressure. Some quite a bit faster than others. For tubed tires it's more to do with the tube than the tire. Latex typically losing air much faster than butyl. One PSI of air every other day isn't unusual if you keep high pressure in narrow tires. Some say even more.
Your difficulties you describe putting air in suggests you either need a different pump or air chuck or perhaps learn or get more skill with what you are doing.