During the placement of a grommet, the grommet is just inserted into a small slit in the drum. The tensile elastic nature of the drum fibres hold it properly. The skin of the deeper part of the external ear canal and that of the eardrum has a great propensity to grow fast and migrate outwards.
It is quite obvious that a foreign body, namely the grommet, also will move along and get extruded. Several different innovations have been tried in designing the grommets, so that they stay in place for a longer term. But, eventually almost all get extruded. Once they get extruded, an evaluation must be done to ascertain whether a grommet is still essential. If so, a new grommet can be inserted. This is a fairly straightforward operation.
Yes, your child can fly with the grommet in place. Only activities which involve getting water into the ear are prohibited, e.g. swimming, diving and head bath. Even during such activities, a good earplug may prove useful.
Caution: A majority of commercial earplugs marketed as swimming gear are not 100 per cent waterproof. Please consult your doctor - he/she will be able to source a silicon earplug for you. This plug is actually silicon putty, which can be put over the external ear and moulded to plug the canal tight. Even though it is expensive to buy, it can be reused up to several months.