About nine years ago I had a Japanese teacher from Osaka, and I'm pretty sure she pronounced 教室【きょうしつ】 as "kyoshtsu", i.e. dropping the "i" in しつ. The reason I remember is that I had trouble learning to say it. But my current teacher, from Niigata, distinctly says the "i". Is this a regional difference, something that varies from person to person, or am I just not remembering it properly?
As pointed out above, the issue here lies in devoicing. In Japanese, high vowels (i and u) undergo devoicing when they are surrounded by other unvoiced sounds. This is extremely common, but it does vary somewhat by region, and to a lesser extent, by person. In standard Japanese, though, it's most common to devoice them.