Can older Walker pumps get weak after running for 30 minutes??

I bought a 2001 MTGHS 48" with a 20 hp Kohler. Hour meter says about 600, but I know that's not right. After running it for 30 mins or less, the left side starts getting weak, pulls to the left, then catches up. It almost feels like slightly pushing in the clutch enough that it starts slipping on the left side, then letting it out all the way. It makes it hard to drive straight. My nearest Walker dealer replaced all the belts, including the drive belt. they let it run for 30+ mins and said...

Can older Walker pumps get weak after running for 30 minutes??