According to Epidemiology of and Diagnostic Strategies for Toxoplasmosis, a Toxoplasma gondii oocyst can survive up for more than a year in a moist environment due to the nature of its cell walls.
However, a cat can only spread the parasite via feces for 1-3 after infection.
Links:
Article Epidemiology of and Diagnostic Strategies for Toxoplasmosis
During a primary infection, the cat can excrete millions of oocysts daily for 1-3 weeks. The oocysts are very strong and may remain infectious for more than one year in warm humid environments.
Once sporulated and when properly stored (not too dirty with fecal material and in 2% sulfuric acid solution at 4 degrees) they can remain viable for years. In my hands even after 3-4 years some oocysts are still infective. I recommend checking their viability though, as the % of viable ones would be low after 1-2 years. There are some publications covering this issue, for example: Article Toxoplasma gondii Oocyst Survival under Defined Temperatures