Just to be clear re: the Expansion pak, it is only needed for certain games; it plugs into the console. You either have the jumper pack (included, sounds like you do) or you have the Expansion pack (which doubles the memory). I'm confused because you said "expansion packs" plural :/ Which makes me think you might be referring to the Controller Pack (the memory cards that go into the controllers). the Expansion pak is required for a half dozen games (Donkey Kong 64 and Perfect Dark being two specifics I can recall). Doom 64 doesn't use the extra memory for anything, just fwiw.
This
Wikipedia article on N64 accessories might clear it up.
For saving games it's either on the game, or uses a Memory Card on the controller.
The game in question, Doom, uses the Memory Card.
If the games are not saving or being persistent, than it's likely the battery on the memory card is dying. You could of course just get another memory card(s) (make sure it's a Controller pack memory card for an N64 and not the expansion pack, though!), but you can also just replace the battery; it's a standard CR2032.
In that regard we can see the link reddevilggg posted; his posting goes under the original notes about the game being an SNES game, as well as using on-cartridge SRAM. I've found that controller packs typically require no extra work; you take it apart and the battery has it's own holder that you can slip a new battery into, and the game should store your saved files again. N64 games (the ones that have battery-backed SRAM on the cartridge, anyway) are often more tricky to deal with because the cartridges are smaller.
(Sidebar on the linked topic: The recommendations for replacing a battery I've seen attempt to be more "future-proof" in that they typically recommend replacing that entire portion with a CR2032 battery holder; so the battery can be easily replaced, which seems reasonable).