No more than 12 years.
To answer this question we can look at the different components' lifetimes to try and decide which one will fail first. Once one area fails, your system will break down. I have provided my own rationalization of factors, however you can find a detailed report of expected LED Traffic Light Lifetimes Here.
1. Solar Panels: 40+ years
Solar panels made after the year 2000 have a degradation rate in efficiency of about 0.5% per year. However the newest solar panels are rated even better.
… a panel manufactured today should produce 92% of its
original power after 20 years
Assuming that the traffic signal was created sometime after 2000 AD, 40 years is a realistic panel lifetime. If 80% or greater efficiency is required to keep the bulbs running, because for example the government was on a budget and used as little solar panel as possible, then the prediction -0.5% / year x 40 years = -20% gives us 80% efficiency after 40 years.
Newer panels could last even longer, but this is not the shortest lived component so further investigation is not necessary.
2. Solar Panel's Battery: 5 - 15 years
The general range for a solar battery's useful lifespan is between 5
and 15 years.
3. Traffic Lights: 1 - 12 years
Typical incandescent traffics lights have been tested and are known to last about 8000 hours. This comes out to about 0.91 years if left on continuously, or double that if used only at night. So these would last somewhere between 1 and 2 years.
A typical incandescent traffic light bulb using 150 watts generally
lasts 8000 hours as studies have shown.
The very best LED light are rated at around 50,000 hours. If they were left on continuously they would last about 5.7 years, or double that if used only at night. So these would last somewhere between 5 and 12 years.
Many LEDs have a rated life of up to 50,000 hours. This is
approximately 50 times longer than a typical incandescent, 20-25 times
longer than a typical halogen, and 8-10 times longer than a typical
CFL. Used 12 hours a day, a 50,000 bulb will last more than 11 years.
4. Copper-Wiring: 20 - 50 years
The standards that cables are manufactured to do not specify a
particular life expectancy. Some cable manufacturers will determine a
likely life expectancy based on typical conditions. For example a
household fixed wiring cable with typical electrical loading, wired
using the appropriate wiring guidelines, could be expected to last 20
years. However, in some cases cables which have not been used
excessively have been found in relatively good condition up to 50
years after installation.
From these facts you should see that the traffic light will likely be where this system fails first. If you are lucky your traffic light might last a decade. However there are at least two different components that are rated to fail in the 5-15 year range, so anything beyond this range is very unlikely. Finally if the traffic light is using a typical incandescent bulb, then it will last even less time and go out after only 1 year.