As mentioned in the comments spring designs and materials can vary widely to it is difficult to generalise.
However if we consider steel springs which are very common then there are a few factors to consider.
Firstly if properly specified a spring should never exceed its elastic limit, however if this does happen then its rate may very well change due to work hardening and early failure is quite likely.
For a spring operating within specification then fatigue is one possible cause of failure this occurs over a large number of cycles within the elastic limit as small local stress concentrations which cause local overloading and gradual crack growth untill the crack reaches a critical length and then propagates very rapidly. The gradual crack growth will have a small effect on the performance of a part as it will reduce its cross section slightly.
Specific materials will have a fatigue limit, this is stress at which a large number of cycles will lead to failure. Some materials have a fatigue limit close enough to the yield stress that fatigue does not need to be considered, in others the limit is so low that any practical component will be subject to fatigue eventually.
Fatigue failures are predicted statistically so you might say that a particular spring has a 99% chance of not failing before 100k cycles and a 50% chance of failing after 500k cycles based on experimental data and empirical formulae so the nominal design life before replacement is a compromise between the consequences of premature failure and the cost of replacement.
Another problem is creep this is plastic type deformation which occurs below the elastic limit when constant loads are applied for long periods.
Both creep and fatigue are generally calculated from empirical data specific to a specific material, manufacturing process and component class.
Another consideration is environmental corrosion and degradation. Metal springs can suffer from corrosion in certain conditions and polymers may break down over time due to UV light and reactions with environmental chemicals.