If you have an idle contract, then eventually it WILL count against you and has the potential to lower your Job Success Score slightly.
Because one of the things that Job Success Scores are calculated from is the percentage of "active" contracts. On your "My Stats", this is shown as "Long-term clients."
What percentage of the clients you CURRENTLY have open contracts for are "long-term", meaning, you have worked for them over a period of more than three months.
In order for that to count, you must have worked for the client three or more months ago AND you must have worked for the client during the past month.
So if a contract is idle for along time, it means the client is NOT a long-term client, because you have not worked for that client during the past month.
The impact of this is not large, but it can prevent you from having your highest-possible JSS, especially as you have more of these... as they represent a larger percentage of your total open contracts.