Can capacitors extend the lifespan of solar batteries?

In short, no. While super capacitors are definitely a technology that could help to extend the life of solar batteries, they cost considerably more than a battery and would not likely be worth the investment at this time.

While super capacitors have been studied for use in solar batteries, they are still not widely used because they are fairly expensive and require more maintenance than traditional batteries. A super capacitor lasts longer than a battery, but it can only handle short, but huge power demands better than a battery could. So they could help a little to increase battery life, but they cost considerably more- so probably not worth it to add them at the present time.

Since many solar batteries are Li-ion, the best way to extend their life would be to avoid over discharge and limit charge to maybe 80% of battery capacity (like Tesla does with their cars). Also limit temperatures of course!