The fact of the matter is that, as a general rule, legally there is no set timetable for how long such an investigation can take. Unless such a timetable was set forth in stated company policy or a union agreement or employment contract.
That having been said, you very well may be eligible for unemployment. At this point, what you need to do now is to contact your state's department of labor about your situation. Further, if you believe that your suspension was the result of actionable discrimination (i.e. discrimination based on being a part of a protected category due to age, race, sex, pregnancy, etc.), you should consult with directly with an employment law attorney in your area.
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