20 year old "Spongy" Roof - It was solid 5 years ago - Do I need new plywood?
Yes, the roof sheathing could go bad (weaken) after a few years due to 1) moisture, 2) extra heavy snow loads

1) Moisture is the most likely problem. Plywood is made from wood veneer plies that are glued together. When moisture seeps into the plies, they will delaminate. The plywood will probably look fine from the attic (looking up) but it will become spongy. 

2) If the plywood is slightly undersized, (half inch thick on joists spaced 24” spacings) it could feel spongy, especially if there have been several extra heavy snowfalls. 

The plywood will loose it’s Modulus of Elasticity (it’s ability to recover from deflection) if loaded to its capacity several times. 

Generally we require 5/8” thick plywood for joists at 24” on center. (1/2” is rated for 24” spacing, but will deflect significantly.) If you live in a “high wind” area or a seismically active area, 5/8” is required. (High wind areas will suck your shingles off your roof without an additional holding power of a minimum of 5/8” thick plywood.)

Note: I doubt only 3 sheets are required. I also doubt a whole sheet will need to be replaced at each problem location. The roofers are going to find more problems and charge you accordingly once the roofing is removed. (Old common roofers trick.) I’d get a unit price for each 4’x8’ sheet and 4’x4’ half sheet that needs to be replaced.