We tend to look at Tefila as a request for divine intervention to solve our most difficult problems and grant us our wishes and dreams. Sadly, as people of the world, we look at tefila as a last resort when we've already done everything we can possibly do through mundane means. At that point we give up and hand the case over to Hashem begging him to perform a miracle. Aside from this being an arrogant approach, since "we" can do nothing and everything turns solely on the will of Hashem be it mundane or miraculous, moreover this signals that our understanding of tefila is fundamentally flawed.
The Maharsha (Kidushin 29b) explains that tefila is not a secret weapon that circumvents the rules of nature, rather tefila is a part and parcel of nature. Hashem created the world with natural rules of cause and effect and tefila fits very much within this framework. Just like when a seed is planted properly the natural occurrence is that a plant will grow, so too when a tefila is said properly quite naturally the request will be granted. That is the way Hashem created nature, even if it is not documented as such in science books.
The gemara tells the story of Rav Acha bar Yaakov who came to the town of Abaye. In Abaye's town no one dared enter the Shul because of a frightening extraterrestrial creature that roamed around inside. Seizing the opportunity to rid themselves of the demon, Abaye made sure all the townspeople did not offer Rav Acha a place to sleep so he would be forced to sleep in the Shul and confront the demon. Abaye was convinced that Rav Acha would be successful in destroying him. And so it was, when Rav Acha was confronted by a seven headed snake, each time he bowed in davening one head was decapitated. The Maharsha asks how did Abaye dare endanger Rav Acha and rely on a Nes? He answers that Abaye did not rely on supernatural protection for Rav Acha, but rather Rav Acha's power of tefila, which he was confident would save Rav Acha and eliminate the monster.
Why don't we see this simple direct relationship? Did you ever plant seeds as a school project? I don't know about you but mine never produced any great harvest. Planting must be done right in order to yield results, and so must tefila. Proper tefila means preparing the tools such as the mouth, heart, and mind. It took a Rav Acha to rid the town of a snake, and even the great tzaddik Abaye did not believe his own tefila was powerful enough to save the Shul.
The fact is that tefila helps in every instance. It is no less natural than bending down and lifting to pick up a rock. Some rocks are heavier and need more power to move them. Sometime we are not strong enough to move the rock all the way but only halfway. The fact is that every tefila helps in a most mundane manner. Tefila can make fluke things happen, put ideas in people's head, cure diseases, and anything else no matter how far beyond the imagination. Just ask for what you need and leave it to Hashem's discretion how to handle it.
The only question is how powerful is our tefila for the task at hand. Even so, not a single tefila goes to waste, and what doesn't yield results here and now may yield results at a later date and time. Keep davening, things are happening!