You may need a new water pump, water pumps have an inestimably life and may give out before other crucial engine components. Research junk yards or salvage yards for used parts as they will be a cheap alternative to new OEM parts. Estimating the life of a water pump is difficult as it is not a "wear" item.
Any water pump should be checked approximately every 35,000 miles that you drive your vehicle. At 60,000 miles it may well be ready to have the pump replaced. Check with your mechanic and ensure it is indeed the pump.