Basically, because people thought it was safe. It didn't seem significant to use the same prime since the key exchange process involves both Alice and Bob generating a secret. Solving the discrete logarithm of g^a mod p was still thought to be intractable given a large enough (1024bits) p.

As to the technical reason why the DH parameters were reused - speed and efficiency. A DH key exchange would take longer if you had to generate those parameters each time.