Suppose I hear a station during a contest that is an eligible contact, but not necessarily a multiplier (worth points, but only a nominal amount of points). This station is relatively faint, (maybe 2-3 S-units above the noise floor) but intelligible. How can I tell if the station is going to be a quick, easy contact or a slow, painful, drawn-out exchange that will hurt my score? When do I cut my time losses and move on to the next station?
Trial and error.
A lot depends on your equipment, antenna, definition of worthwhile. Also, the band and propagation conditions. The cool thing about HF is that while he might be faint to you, how he hears you could be completely different.
For me personally, they typically need to be 3 S units up for a smooth exchange, but other folks have had other answers.
In telephony, speech quality is reduced to a number, such as a PESQ score. Which is not to say that radio amateurs should start using formal methods from telephony, but to highlight that the need to put a number on the quality of reception exists, and there are ways to do it. Once you have a number obtained in some consistent way, then you can easy set a limit, like "anything less than 1.0 is effectively out of coverage".
Any kind of formal method would require the station to transmit some known standard sample of voice. You have to control the input and measure the output.
If you don't control what is transmitted, then it's purely subjective.