Ijust need a couple reasons. why might some kinds of living things undergo sexual reproduction at times when conditions in their environment become less favorable?

This form of reproduction leads to more genetic variability and higher chances of survival.

When conditions in the environment become less favorable, the form of reproduction becomes preferable because it increases the chances of the offspring surviving.

Offspring of such reproduction are genetically more diverse than their parents, unlike those from other  reproduction which are of the same genetic composition as their parents.

With more variability, the offspring have a higher chance of surviving the unfavorable environment than their parents.

More on advantages of reproduction can be found here: link

Because of adaptation (genetic variation).

Explanation:

Some organisms might undergo sexual reproduction at times when conditions aren't favorable, because the offspring will start adapting, so that what was once a "less favorable" condition, is now more favorable.

The goal of all that, is basically to create a genetic variation that consists in making the individuals better adapted to the environment: to make the environment more favorable.

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→ Keep in mind that, the environment doesn't change at all, what changes is how the organisms react to it.

For example, imagine that your punch is the environment, and that wood was the previous set of organisms, and that iron is the second set of organisms. If you punch both of them (given that your punch doesn't change), you'll note that there is a difference between punching wood and iron. The punch wont change, but how the material (which in this case represents our organisms) reacts to the punch, does change.

Hope it helped,

BiologiaMagister