The continues will carry through the game and are also stored with the level codes. So if you have no credits left when you get the code the restart will have no credits either.
It can be a bit hard! One strategy is to try and gain some extra credits through extra points, especially early on in the game, and to build up your ammo levels. Level 4 and 5 are good for picking up extra guns and ammo because of the bonuses on those levels, useful for level 6.