Does an Ethernet link get gradually slower as the cable run gets longer?

Not in the sense of a hosepipe simply delivering less and less speed with every extra metre. Ethernet equipment negotiates a link rate, while the cabling has to keep attenuation, crosstalk, delay and the other transmission parameters within the limits needed for that application.

Longer cable does increase loss and reduces the available margin. Push the channel beyond what the application and cabling can support and you may get errors, instability or a lower negotiated speed rather than a neat percentage reduction for every metre.