Depending on the type of person you are, being faced with a crisis or rough period in life usually results in one of two things: you start ignoring your religious duties, or you increase them ten-fold, hoping for that nudge of divine assistance. In general, the ancient Hellenes chose option number two. Bad weather threatening the crops? Conduct an elaborate festival to Zeus Ombrios. Had an earthquake? Visit the Oracle of Delphi and have a ritual to the designated God or Goddess to appease Them and stop it from happening again. No doubt, familial issues were also put before the Gods as well.

A fictional account noted down by famed writer Alciphron describes one such sacrifices to Zeus Ombrios, even though this one was in vain:

"A drought is upon us. Not a cloud is to be seen in the sky, and we want a regular downpour. You have only to look at the ploughed land to see how dreadfully parched the soil is. I am afraid all our sacrifixes to Jupiter Pluvius [Zeus Ombrios] have gone for nothing, and yet all we villagers outdid each other to make a good sacrificial show. Each man brought what he could according to his means and ability. One brought a ram, another a goat, another some fruit, the poor man brought a cake, and the positive pauper some lumps of decidedly mouldy incense. No one could run to a bull, for our Attic soil is thin and cattle are scarce. But we might have saved our expense. Zeus it would seem is 'on a journey' and cannot attend to us."
From this account it becomes clear that while prayer and sacrifice during troubled times were encouraged and oft practiced, no one assumed success of said sacrifices. The Gods do not always answer our prayers, and they are not always appeased by our sacrifices. It depends on our kharis, Their plan for us, and most likely a myriad of other factors far beyond our influence, reach, and understanding. Yet, we are always encouraged to enter ritual, to make our sacrifices, and to pray.

There are accounts of an enormous scope of rituals and rites practiced in ancient Hellas to sway the Gods in the favour of their followers. Everything from two men running around the vineyard in opposite directions with a black cock that has been cut in two to banish harmful winds, to abstaining from sex, certain foods, or certain practices to ward of illness, and the more traditional sacrifices that have the potential to solve pretty much anything if the Gods are so inclined. Not all of them are successful, and not all of them are successful all the time, but because they sometimes are and always have the potential to be, they are practiced.

Prayer--even if unanswered in the end--give us a beautiful return on investment, regardless: prayer helps us feel in control of the situation at hand, we accept it more readily because we can put the responsibility of a good outcome in the hands of a third party, and it gives us hope that everything will work out in the end. Yes, this can make you fight a little less hard for your own happy ending, but when faced with natural disasters, illness, or other seemingly unsurmountable obstacle, it's often preferred to find an outlet for the anxiety that arises.