Technically the rovers are only supposed to last for about a martian year (3 Earth yrs) but in actuality the engineers design the components to last much longer. Why? Well NASA virtually always gives funding to extend the lifetime of the mission. Opportunity, for example, was supposed to last 90 days but ended up surviving 14 years until a dust storm killed it off.

Curiosity and Perseverance's lifetime is limited by its power source, which is fueled by the decay of radioactive elements. This is only going to last 10-15 years before the rover runs out of power - for reference Curiosity is 10 years old and Perseverance is 1 year old. Once they run out of power, their instruments become irreperably damaged by the cold winter temperature.

So people definitely won't make it in time to save Curiosity, but perhaps we could greet Perseverance :)