I have a 60hp merc bigfoot 2005 4cycle motor. I am having trouble keeping the fuel flowing. The bulb gets hard when pumped, but will not stay hard when running. I have to pump it back up to keep it running. I have changed the fuel pump, and it seemed to solve the problem for one day, but the next day I started having the same problem. Is there a possibility the new fuel pump is bad, or is there something else to look for? Bill T

I have been through a lot of fuel issues lately. I would install a "temporary" clear piece of plastic tubing as the last piece before it goes into the engine. Not very long just a couple of inches will do. What you are trying to do is look for air bubbles past all the fittings and primer bulb going into the engine. Please do not leave this plastic piece in place too long because it will eventually fail.
If you see bubbles in the "sight window" you need to go over all the fittings and make adjustments where needed. Just from experience I replace the primer bulb every spring and keep a spare on-board just-in-case. IMHO the Mercury branded primer is the best.

Don't take offense but make sure the arrow on the bulb is pointed to the engine.

try new bulb and tank and fuel lines

I would check your tank and supply hose. If they are old, replace them both. Old hoses can scale off on the inside, and can even close down when suction is applied. Also, crap can build up inside your tank over the years. New ones aren't too expensive.