First, I'd look to the practical solution -- can the dish simply be relocated off of the common area to your premises?
You don't give many specifics about your CC&Rs and the basis for your HOA to fine you. Nonetheless, the Telecommunications Act of 1996 will often prohibit restrictions on placement of direct broadcast satellite dishes. I'd start by determining whether your HOA's rule restricting the placement of the dish is compliant with this federal law first. Of course if the dish is placed on common area rather than property owned by you or under your exclusive control, the Telecommunications Act probably won't help.
Next, I'd look to your lease. If it's well drafted, it should require the tenant to comply with the CC&Rs and make the tenant liable for any breaches, including the payment of fines imposed by the HOA as a result of the tenant's conduct. In other words, if your lease is well drafted, you may be able to pass the costs of the violation on to your tenant.
Finally, you may want to consider challenging the fine. pursuant to Chapter 116 of the Nevada Revised Statutes, you are probably entitled to notice and a hearing before a fine is imposed. $400 per month sounds awfully steep, and you may be able to challenge the fine simply on the basis that it is unreasonably large.
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The answer to your question is probably in your contract. Read through it. It may be that your recourse is to evict the tenant. Also, you should go to an HOA board meeting and ask if it will hold off on the fines until you can fix the situation. Sometimes HOA boards are quite reasonable.
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