Remain means:
1)"To continue to be in a particular situation or condition" For example: The economy remains fragile.
2)"To continue to be something, even after a long period of time." For example: Japan’s low crime rate remains the envy of the industrialized world.
3)"To have a particular attitude, opinion, or belief and not change it." For example: Andrew remained firm in his belief that the policy was wrong.
Maintaim means:
1)"To make something stay the same." For example: It’s sometimes hard to maintain the right balance between your work and your home life.
2)"To continue to communicate with someone and not allow a relationship to end." For example: Though now in government, he has maintained close contact with his former colleagues in the oil industry.
3)"To make sure that something stays at the same level, rate, or standard." For example: Some schools experienced difficulty in maintaining staffing levels.
Then, "Remain in your position" and "Maintain the container on the board" is correct.