Is it a proper use of a semi-colon to use it for joining two related but non-complete sentences? For example, it is correct to say "you should run every day; it will help you stay fit."

How about the following?

Run every day; stay fit.
laketunaRun every day; stay fit.
Yes. Those are complete sentences.
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"Run every day" and "stay fit" are complete sentences? I was referring to full sentences where there are at least a subject and a noun when I wrote "complete sentences."

Anyway, I was originally asking about the semi-colon usage. What do you think?
laketuna"Run every day" and "stay fit" are complete sentences?
Yes, they are. They’re called imperative sentences, in which the subject is understood as you. They aren’t subordinate clauses, and they can be coordinated by semicolons just as declaratives can.