Some answers have claimed that much of the time is not an idiomatic phrase, and/or that it is restricted to particular meanings. However, Google claims around 171 million results for the phrase. While some of these are part of other phrases ("How much of the time", "so much of the time"), looking at the first few pages of results suggests that "much of the time" is a common idiomatic phrase, and that the contexts where it can be used don't differ significantly from "most of the time".
COCA shows a similar picture (494 occurrences, some of which as part of other phrases, but most not - though contrasted with 3655 occurrences of "most of the time"). So it exists, but is much less common than "most of the time".
My own experience, which seems to match the examples I've found from both sources, is that "most of the time", while technically correct for anything that occurs more than 50% of the time, tends to be used for things that occur much more than 50% of the time. The phrase "much of the time", then, conveys a sense of something that happens frequently, or for a significant proportion of the time, but not enough to call it "most of the time".