Yes.
Tension and compression stresses are both major factors in permanently altering the molecular bonds that give elastomers their characteristic elasticity (oxidation being the other). Once those bonds are modified they usually cannot be restored and the elastic properties of the material are permanently compromised.
To minimize such deterioration, store the belt flat and relaxed in a cool, dry place out of direct sunlight. For the fanatic, oxidation could be prevented by storing in a vacuum chamber or in a container whose air has been displaced by a noble gas, helium being the most effective, safest and easiest to obtain. Stored in such conditions, many elastomers would retain their original properties almost indefinitely.
