That's actually not a primer. It's a purge bulb. PULLS gas through the carb when the bulb pops back up. This purges air out of the carb and lines for quicker starting after the saw has sat for a while (or after it has been ran dry). If the bulb is staying 'down' then either it's deteriorated (doesn't have any 'spring' left to it) or the carb is bunged up. Could well be the TINY little screen in the carb. Once it's plugged, the purge bulp can't pull fuel through it. May want to check the filter on the in-tank line too. My money's on the carb however. Pull it apart, clean it, and rebuild it. Make a note of which lines go where before pulling them off of the carb and bulb however....