HOAs that allow short-term rentals (AirBnB) - issues?

This is the board's fault.

The trend seems to be towards amending Declarations to restrict STRs, not allow them.

Better act fast. The more condos owned by STR landlords, the lower chances of amending the Declaration.

This topic comes up here a lot and has received much treatment in the courts and by the media, especially lately with the wild ride of the housing market, with crazed investors believing there will be a housing shortage.

Allowing STRs would require an amendment to the CC&Rs that is approved by a majority of homeowners, and often a super-majority of 67% or 75%. So it's by no means a done deal if only a small group of owners want this. Educate the community before any amendment is attempted, because some states forbid "campaigning" by the board or association attorney.

What percentage of your homes are currently rentals? There seems to be a sweet spot beyond which the community is no longer able to control rental numbers (because of the above).

You're right to be concerned. Lenders shy away from communities with too many rentals. Buyers can as well. There are real benefits to living in a community that is mostly owner occupied, and property values can drop as a community becomes less attractive to those buyers. If you have amenities such as a pool or clubhouse, at some point these will probably have to be re-classified as public and will need to be ADA-compliant - if they aren't already, you may have to renovate which everyone will have to pay for just in order to benefit this small group - so be sure to include this expense in the reasons why this isn't a good idea. (Ask the association's attorney about ADA and public facilities.)

If you're lucky, either your CC&Rs or your state laws prohibit commercial use of condominium property. Or your zoning laws may have something to say. A number of courts have held that STRs are commercial since they often require the owner to have a business license and pay lodging tax. One judge's reasoning for this ruling is that, unlike with traditional rentals, someone staying in an STR can't claim to actual live there in any reasonable interpretation of "live" - the person doesn't list the STR as their permanent address, they don't receive mail there, and the bulk of their personal belongings are elsewhere. This interpretation of commercial isn't universal, though.

If all else fails, I recommend that boards make the economics of rental property work against the owners. Many operate with pretty thin margins, and if they spend more than they're taking in, they don't have a viable business. So yes, enforce your CC&Rs, especially and including nuisance restrictions. Fine the owner for all violations. Call the owner to hearings for each violation. Convince the owner that he won't be able to just kick back and rake in the dough while everybody else pays the price.