It is said that all ships by the time of Victory have Minovsky Craft Systems that allow them to fly in atmosphere. However, the only time I recall the Reinforce
leaving Earths atmosphere, in episode 16, it was towed up by a Salamis Kai
fitted with a booster. Since the Reinforce
is said to be an older ship that wasn't still in use, perhaps it wasn't equipped with the system, like the active duty Salamis Kai
(And other older EFSF ships shown flying later on).
For what it's worth, later in the series the White Ark
requires a booster even though it has the MCS, but I'd chalk that up to it's small size, and the Reinforce Junior
is shown without one, but it isn't clearly shown flying back into space, so it's hard to say one way or another.