How long do evaporator coils last in a home AC system?
They should last for the life of the A/C system, which is generally 15-20 years for a high quality system. (Many people end up replacing their systems between 12 and 15 years due to efficiency issues or deferred maintenance causing damage to more easily damaged components, such as the compressor.) 

Most of the time, evaporator coils fail because they are allowed to get dirty or are allowed to have ice build up on them. Things you can do yourself to help prolong the life is to make sure you change your HVAC intake filter regularly and use a high quality filter (filters should be in place for no more than a month, and should be replaced sooner in a dusty environment if you can no longer see light through the filter), and make sure that your evaporator coils are draining correctly. 

The easiest way to make them last longer is to have a licensed HVAC technician perform regular maintenance on your system. This should be done once a year, typically in the winter time. The technician will clean the coils and check them over. At the same time, the A/C tech will check to make sure that your coolant is at the right level/pressure and that there are no leaks in your system. 

If you replace them, you probably want to replace the entire system at this point thanks to many recent gains made in efficiency.