Voyager would have needed to harvest raw materials (possibly asteroids) or dedicated some of its own internal structure to be re-processed into shuttle components. The mines might have had a cloaked reserve of spare matter, or had limited quantities of raw materials on board.
Starships have the capability of using a Bussard ramscoop - they deploy a magnetic field to collect interstellar hydrogen.
My understanding (and rationalization) of a starship's fuel lifecycle is as follows:
1) Ship collects interstellar hydrogen.
2) Some of this hydrogen is stored. Some of it is fused to create impulse power. Some of it is fused and the energy used to make antimatter, which is stored.
3) When needed, the stored hydrogen and antimatter are used to fuel the warp core.
If you aren't trying to be stealthy, you can run the ramscoop all the time, and basically never run out of fuel.
This kind of path is absolutely necessary for the operation of any vessel for any significant period of time away from starbases, as otherwise you run out of antimatter, and are stuck.