A preferred method of writing is often to use as little extra words as possible. In this case, not using "the" is grammatically correct since people are relying on internet services. Using "the" is more awkward and not necessary. Also, at the end of the sentence there is the phrase "people's life", but since "people" refers to multiple persons, the word "life" should be replaced with "lives", so the phrase would read, "heavy reliance on internet services in people's daily lives".
Although you should try not to use too many excess words, the question of whether or not to emphasize "internet services" with the article "the" depends on the first part of the sentence.