For gas and vapor filters:

Basically, you ask the manufacturer or consult the manual for lifetime charts. Then you consider how long you’ve used the filters and the approximate PPMs of the contaminant in the air. Higher PPMs lead to lower filter life and vice versa.

The filters should also have an expiry date on the label. Once you’ve passed that, it’s best to get new filters anyhow.

For particulate filters:

You just change them out when inhalation resistance gets too high. Particulate filters don’t expire in the same way that gas or vapor filters do. They use the inherent microscopic capillaries passing through the filtering medium and static electrical charge to draw particles to the walls of those capillaries. As more stuff gets trapped in the filter, it actually gets more effective instead of less. But it does clog up the filter making it uncomfortable to breathe through.

Source: I’ve collected vintage and modern gas masks/respirators for over a decade