On a one-piece, single-car door that's rarely opened (springs usually stretched), do they eventually stretch, thus stopping the opener from working?
Not usually, the spring will loose some tension, but not much. What CAN happen is the spring can break where it attaches to the pully, and in that case, you will loose all spring lift help.
What I see happen more often is the opener needs lubrication, so it gets slower and slower till it can't lift the door at all. Get some garage door opener lube, and lubricate the guides, the screw or any moving parts that much be sliding past each other. This varies depending on wether you have a belt, chain or screw drive. In screw drive, the screw is the main thing that needs lubrication, in the case of a chain, the chain and the channel need lube, and in the case of a belt, only the channel needs lube. Use the right lube, as you have plastic parts that need to not be damaged by the grease. The grease is sold anywhere you can buy garage door openers (home improvement stores).