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Your by-laws need to be a little more specific about what type of permission must be given in order to be enforceable.
An example of enforceable restrictions on rental would be "a maximum of 20% of units may be rental units, a wait list can be established and maintained by the board or management company, units must be owner occupied for a minimum of 12 months prior to being rental units"
An example of unenforceable restrictions would be "rental units are permitted at board discretion"
If the board is permitted to grant or withhold permission for rentals, this is an unenforceable restriction, and therefore you could challenge a board decision denying your rental application
(I would suggest against simply renting the unit out and ignoring the process altogether, follow the by-laws procedure for challenging a board decision, and if necessary a court action against the HOA
challenging the board decision - this is based on breach of contract and violation of the state common interest development act for "arbitrary and capricious" (also called "selective") enforcement).