I would have to respectfully disagree. It should be exactly the opposite: ONLY the game dog has the right to a count. The dog that hesitates loses right there. Only if the dog is really trying to get there, does he then have 10 seconds to do so ... and if he can't, then he loses because in this case he's clearly too injured to continue.
First of all, any knowledgeable dogman is going to know the difference between a dog counted out trying to scratch (but so injured he can't get there), and a dog standing there "taking" a count. (If people don't know the difference, then there is no cure for this kind of cluelessness.) If anything, I believe what should be eliminated in our sport is the MISREADING of the original rules. In the original rules, there is no "count" over a hesitating dog; if a dog takes a 1-count, it loses right there. Ideally, the dog either wants to continue immediately, or it does not.
As I said in the last example, if you think about it in boxing terms, this is easy to understand. If a man gets knocked on his ass, the ref is going to start counting to 10, and the man has 10 seconds to get up. Now, he may be wobbly, stumbling and falling, but if he is trying to get up, then the ref will proceed to continue to verbalize the full 10-count ... but if the boxer just sits there and "takes" the count, shaking his head "no," the ref is going to stop counting and waive the fight over right there. No ref is going to keep counting over a fighter just sitting there consciously refusing to continue.
Jack