Well, a fuel primer bulb isn't part of the factory fuel system. So I can't say if it should stay hard or not. But if it is getting soft, you may have a leak at the carbs, or fuel enriching system.
Also, I wasn't asking about the spark plugs... I was asking if there is a spark. if you have a bad stator, you wont have spark.
It takes 3 things to make it run. (spark, fuel, compression) so before we can figure out why its not running, we need to know what is wrong..